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Theorem aannenlem2 22590

Description: Lemma for aannen 22592. (Contributed by Stefan O'Rear, 16-Nov-2014.)

**Hypothesis**
Ref	Expression
aannenlem.a	Poly $/\$ deg $/\$ coeff

**Assertion**
Ref	Expression
aannenlem2

Distinct variable group:

Allowed substitution hints:

(

)

Proof of Theorem aannenlem2 Dummy variables

are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		simp3 997	. . . . . . . . . 10 Poly $\$ $/\$ $/\$
2		eldifi 3608	. . . . . . . . . . . . . 14 Poly $\$ Poly
3	2	adantr 465	. . . . . . . . . . . . 13 Poly $\$ $/\$ Poly
4	3	3adant2 1014	. . . . . . . . . . . 12 Poly $\$ $/\$ $/\$ Poly
5		eldifsni 4137	. . . . . . . . . . . . . . 15 Poly $\$
6	5	adantr 465	. . . . . . . . . . . . . 14 Poly $\$ $/\$
7		0nn0 10811	. . . . . . . . . . . . . . . . . 18
8		dgrcl 22496	. . . . . . . . . . . . . . . . . . 19 Poly deg
9	3, 8	syl 16	. . . . . . . . . . . . . . . . . 18 Poly $\$ $/\$ deg
10		prssi 4167	. . . . . . . . . . . . . . . . . 18 $/\$ deg deg
11	7, 9, 10	sylancr 663	. . . . . . . . . . . . . . . . 17 Poly $\$ $/\$ deg
12		ssrab2 3567	. . . . . . . . . . . . . . . . . 18 deg coeff
13	12	a1i 11	. . . . . . . . . . . . . . . . 17 Poly $\$ $/\$ deg coeff
14	11, 13	unssd 3662	. . . . . . . . . . . . . . . 16 Poly $\$ $/\$ deg deg coeff
15		nn0ssre 10800	. . . . . . . . . . . . . . . . 17
16		ressxr 9635	. . . . . . . . . . . . . . . . 17
17	15, 16	sstri 3495	. . . . . . . . . . . . . . . 16
18	14, 17	syl6ss 3498	. . . . . . . . . . . . . . 15 Poly $\$ $/\$ deg deg coeff
19		fvex 5862	. . . . . . . . . . . . . . . . 17 deg
20	19	prid2 4120	. . . . . . . . . . . . . . . 16 deg deg
21		elun1 3653	. . . . . . . . . . . . . . . 16 deg deg deg deg deg coeff
22	20, 21	ax-mp 5	. . . . . . . . . . . . . . 15 deg deg deg coeff
23		supxrub 11520	. . . . . . . . . . . . . . 15 deg deg coeff $/\$ deg deg deg coeff deg deg deg coeff
24	18, 22, 23	sylancl 662	. . . . . . . . . . . . . 14 Poly $\$ $/\$ deg deg deg coeff
25	18	adantr 465	. . . . . . . . . . . . . . . 16 Poly $\$ $/\$ $/\$ deg deg coeff
26		fveq2 5852	. . . . . . . . . . . . . . . . . . . 20 coeff coeff
27		abs0 13092	. . . . . . . . . . . . . . . . . . . 20
28	26, 27	syl6eq 2498	. . . . . . . . . . . . . . . . . . 19 coeff coeff
29		c0ex 9588	. . . . . . . . . . . . . . . . . . . . 21
30	29	prid1 4119	. . . . . . . . . . . . . . . . . . . 20 deg
31		elun1 3653	. . . . . . . . . . . . . . . . . . . 20 deg deg deg coeff
32	30, 31	ax-mp 5	. . . . . . . . . . . . . . . . . . 19 deg deg coeff
33	28, 32	syl6eqel 2537	. . . . . . . . . . . . . . . . . 18 coeff coeff deg deg coeff
34	33	adantl 466	. . . . . . . . . . . . . . . . 17 Poly $\$ $/\$ $/\$ $/\$ coeff coeff deg deg coeff
35		0z 10876	. . . . . . . . . . . . . . . . . . . . . . 23
36		eqid 2441	. . . . . . . . . . . . . . . . . . . . . . . 24 coeff coeff
37	36	coef2 22494	. . . . . . . . . . . . . . . . . . . . . . 23 Poly $/\$ coeff
38	3, 35, 37	sylancl 662	. . . . . . . . . . . . . . . . . . . . . 22 Poly $\$ $/\$ coeff
39	38	ffvelrnda 6012	. . . . . . . . . . . . . . . . . . . . 21 Poly $\$ $/\$ $/\$ coeff
40		nn0abscl 13119	. . . . . . . . . . . . . . . . . . . . 21 coeff coeff
41	39, 40	syl 16	. . . . . . . . . . . . . . . . . . . 20 Poly $\$ $/\$ $/\$ coeff
42	41	adantr 465	. . . . . . . . . . . . . . . . . . 19 Poly $\$ $/\$ $/\$ $/\$ coeff coeff
43		simplr 754	. . . . . . . . . . . . . . . . . . . . 21 Poly $\$ $/\$ $/\$ $/\$ coeff
44	9	ad2antrr 725	. . . . . . . . . . . . . . . . . . . . 21 Poly $\$ $/\$ $/\$ $/\$ coeff deg
45	3	ad2antrr 725	. . . . . . . . . . . . . . . . . . . . . 22 Poly $\$ $/\$ $/\$ $/\$ coeff Poly
46		simpr 461	. . . . . . . . . . . . . . . . . . . . . 22 Poly $\$ $/\$ $/\$ $/\$ coeff coeff
47		eqid 2441	. . . . . . . . . . . . . . . . . . . . . . 23 deg deg
48	36, 47	dgrub 22497	. . . . . . . . . . . . . . . . . . . . . 22 Poly $/\$ $/\$ coeff deg
49	45, 43, 46, 48	syl3anc 1227	. . . . . . . . . . . . . . . . . . . . 21 Poly $\$ $/\$ $/\$ $/\$ coeff deg
50		elfz2nn0 11772	. . . . . . . . . . . . . . . . . . . . 21 deg $/\$ deg $/\$ deg
51	43, 44, 49, 50	syl3anbrc 1179	. . . . . . . . . . . . . . . . . . . 20 Poly $\$ $/\$ $/\$ $/\$ coeff deg
52		eqid 2441	. . . . . . . . . . . . . . . . . . . 20 coeff coeff
53		fveq2 5852	. . . . . . . . . . . . . . . . . . . . . . 23 coeff coeff
54	53	fveq2d 5856	. . . . . . . . . . . . . . . . . . . . . 22 coeff coeff
55	54	eqeq2d 2455	. . . . . . . . . . . . . . . . . . . . 21 coeff coeff coeff coeff
56	55	rspcev 3194	. . . . . . . . . . . . . . . . . . . 20 deg $/\$ coeff coeff degcoeff coeff
57	51, 52, 56	sylancl 662	. . . . . . . . . . . . . . . . . . 19 Poly $\$ $/\$ $/\$ $/\$ coeff degcoeff coeff
58		eqeq1 2445	. . . . . . . . . . . . . . . . . . . . 21 coeff coeff coeff coeff
59	58	rexbidv 2952	. . . . . . . . . . . . . . . . . . . 20 coeff deg coeff degcoeff coeff
60	59	elrab 3241	. . . . . . . . . . . . . . . . . . 19 coeff deg coeff coeff $/\$ degcoeff coeff
61	42, 57, 60	sylanbrc 664	. . . . . . . . . . . . . . . . . 18 Poly $\$ $/\$ $/\$ $/\$ coeff coeff deg coeff
62		elun2 3654	. . . . . . . . . . . . . . . . . 18 coeff deg coeff coeff deg deg coeff
63	61, 62	syl 16	. . . . . . . . . . . . . . . . 17 Poly $\$ $/\$ $/\$ $/\$ coeff coeff deg deg coeff
64	34, 63	pm2.61dane 2759	. . . . . . . . . . . . . . . 16 Poly $\$ $/\$ $/\$ coeff deg deg coeff
65		supxrub 11520	. . . . . . . . . . . . . . . 16 deg deg coeff $/\$ coeff deg deg coeff coeff deg deg coeff
66	25, 64, 65	syl2anc 661	. . . . . . . . . . . . . . 15 Poly $\$ $/\$ $/\$ coeff deg deg coeff
67	66	ralrimiva 2855	. . . . . . . . . . . . . 14 Poly $\$ $/\$ coeff deg deg coeff
68	6, 24, 67	3jca 1175	. . . . . . . . . . . . 13 Poly $\$ $/\$ $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
69	68	3adant2 1014	. . . . . . . . . . . 12 Poly $\$ $/\$ $/\$ $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
70		neeq1 2722	. . . . . . . . . . . . . 14
71		fveq2 5852	. . . . . . . . . . . . . . 15 deg deg
72	71	breq1d 4443	. . . . . . . . . . . . . 14 deg deg deg coeff deg deg deg coeff
73		fveq2 5852	. . . . . . . . . . . . . . . . . 18 coeff coeff
74	73	fveq1d 5854	. . . . . . . . . . . . . . . . 17 coeff coeff
75	74	fveq2d 5856	. . . . . . . . . . . . . . . 16 coeff coeff
76	75	breq1d 4443	. . . . . . . . . . . . . . 15 coeff deg deg coeff coeff deg deg coeff
77	76	ralbidv 2880	. . . . . . . . . . . . . 14 coeff deg deg coeff coeff deg deg coeff
78	70, 72, 77	3anbi123d 1298	. . . . . . . . . . . . 13 $/\$ deg deg deg coeff $/\$ coeff deg deg coeff $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
79	78	elrab 3241	. . . . . . . . . . . 12 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
80	4, 69, 79	sylanbrc 664	. . . . . . . . . . 11 Poly $\$ $/\$ $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
81		simp2 996	. . . . . . . . . . 11 Poly $\$ $/\$ $/\$
82		fveq1 5851	. . . . . . . . . . . . 13
83	82	eqeq1d 2443	. . . . . . . . . . . 12
84	83	rspcev 3194	. . . . . . . . . . 11 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
85	80, 81, 84	syl2anc 661	. . . . . . . . . 10 Poly $\$ $/\$ $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
86		fveq2 5852	. . . . . . . . . . . . 13
87	86	eqeq1d 2443	. . . . . . . . . . . 12
88	87	rexbidv 2952	. . . . . . . . . . 11 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
89	88	elrab 3241	. . . . . . . . . 10 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
90	1, 85, 89	sylanbrc 664	. . . . . . . . 9 Poly $\$ $/\$ $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
91		prfi 7793	. . . . . . . . . . . . . . 15 deg
92		fzfi 12056	. . . . . . . . . . . . . . . . 17 deg
93		abrexfi 7818	. . . . . . . . . . . . . . . . 17 deg deg coeff
94	92, 93	ax-mp 5	. . . . . . . . . . . . . . . 16 deg coeff
95		rabssab 3569	. . . . . . . . . . . . . . . 16 deg coeff deg coeff
96		ssfi 7738	. . . . . . . . . . . . . . . 16 deg coeff $/\$ deg coeff deg coeff deg coeff
97	94, 95, 96	mp2an 672	. . . . . . . . . . . . . . 15 deg coeff
98		unfi 7785	. . . . . . . . . . . . . . 15 deg $/\$ deg coeff deg deg coeff
99	91, 97, 98	mp2an 672	. . . . . . . . . . . . . 14 deg deg coeff
100	99	a1i 11	. . . . . . . . . . . . 13 Poly $\$ $/\$ deg deg coeff
101		ne0i 3773	. . . . . . . . . . . . . . 15 deg deg deg coeff deg deg coeff
102	22, 101	ax-mp 5	. . . . . . . . . . . . . 14 deg deg coeff
103	102	a1i 11	. . . . . . . . . . . . 13 Poly $\$ $/\$ deg deg coeff
104		xrltso 11351	. . . . . . . . . . . . . 14
105		fisupcl 7925	. . . . . . . . . . . . . 14 $/\$ deg deg coeff $/\$ deg deg coeff $/\$ deg deg coeff deg deg coeff deg deg coeff
106	104, 105	mpan 670	. . . . . . . . . . . . 13 deg deg coeff $/\$ deg deg coeff $/\$ deg deg coeff deg deg coeff deg deg coeff
107	100, 103, 18, 106	syl3anc 1227	. . . . . . . . . . . 12 Poly $\$ $/\$ deg deg coeff deg deg coeff
108	14, 107	sseldd 3487	. . . . . . . . . . 11 Poly $\$ $/\$ deg deg coeff
109	108	3adant2 1014	. . . . . . . . . 10 Poly $\$ $/\$ $/\$ deg deg coeff
110		eqidd 2442	. . . . . . . . . 10 Poly $\$ $/\$ $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
111		breq2 4437	. . . . . . . . . . . . . . . 16 deg deg coeff deg deg deg deg coeff
112		breq2 4437	. . . . . . . . . . . . . . . . 17 deg deg coeff coeff coeff deg deg coeff
113	112	ralbidv 2880	. . . . . . . . . . . . . . . 16 deg deg coeff coeff coeff deg deg coeff
114	111, 113	3anbi23d 1301	. . . . . . . . . . . . . . 15 deg deg coeff $/\$ deg $/\$ coeff $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
115	114	rabbidv 3085	. . . . . . . . . . . . . 14 deg deg coeff Poly $/\$ deg $/\$ coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
116	115	rexeqdv 3045	. . . . . . . . . . . . 13 deg deg coeff Poly $/\$ deg $/\$ coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
117	116	rabbidv 3085	. . . . . . . . . . . 12 deg deg coeff Poly $/\$ deg $/\$ coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
118	117	eqeq2d 2455	. . . . . . . . . . 11 deg deg coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
119	118	rspcev 3194	. . . . . . . . . 10 deg deg coeff $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff
120	109, 110, 119	syl2anc 661	. . . . . . . . 9 Poly $\$ $/\$ $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff
121		cnex 9571	. . . . . . . . . . 11
122	121	rabex 4584	. . . . . . . . . 10 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
123		eleq2 2514	. . . . . . . . . . 11 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff
124		eqeq1 2445	. . . . . . . . . . . 12 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff
125	124	rexbidv 2952	. . . . . . . . . . 11 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff
126	123, 125	anbi12d 710	. . . . . . . . . 10 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff $/\$ Poly $/\$ deg $/\$ coeff Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff
127	122, 126	spcev 3185	. . . . . . . . 9 Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff $/\$ Poly $/\$ deg deg deg coeff $/\$ coeff deg deg coeff Poly $/\$ deg $/\$ coeff $/\$ Poly $/\$ deg $/\$ coeff
128	90, 120, 127	syl2anc 661	. . . . . . . 8 Poly $\$ $/\$ $/\$ $/\$ Poly $/\$ deg $/\$ coeff
129	128	3exp 1194	. . . . . . 7 Poly $\$ $/\$ Poly $/\$ deg $/\$ coeff
130	129	rexlimiv 2927	. . . . . 6 Poly $\$ $/\$ Poly $/\$ deg $/\$ coeff
131	130	impcom 430	. . . . 5 $/\$ Poly $\$ $/\$ Poly $/\$ deg $/\$ coeff
132		eleq2 2514	. . . . . . . . 9 Poly $/\$ deg $/\$ coeff Poly $/\$ deg $/\$ coeff
133	87	rexbidv 2952	. . . . . . . . . . 11 Poly $/\$ deg $/\$ coeff Poly $/\$ deg $/\$ coeff
134	133	elrab 3241	. . . . . . . . . 10 Poly $/\$ deg $/\$ coeff $/\$ Poly $/\$ deg $/\$ coeff
135		simp1 995	. . . . . . . . . . . . . . 15 $/\$ deg $/\$ coeff
136	135	anim2i 569	. . . . . . . . . . . . . 14 Poly $/\$ $/\$ deg $/\$ coeff Poly $/\$
137	71	breq1d 4443	. . . . . . . . . . . . . . . 16 deg deg
138	75	breq1d 4443	. . . . . . . . . . . . . . . . 17 coeff coeff
139	138	ralbidv 2880	. . . . . . . . . . . . . . . 16 coeff coeff
140	70, 137, 139	3anbi123d 1298	. . . . . . . . . . . . . . 15 $/\$ deg $/\$ coeff $/\$ deg $/\$ coeff
141	140	elrab 3241	. . . . . . . . . . . . . 14 Poly $/\$ deg $/\$ coeff Poly $/\$ $/\$ deg $/\$ coeff
142		eldifsn 4136	. . . . . . . . . . . . . 14 Poly $\$ Poly $/\$
143	136, 141, 142	3imtr4i 266	. . . . . . . . . . . . 13 Poly $/\$ deg $/\$ coeff Poly $\$
144	143	ssriv 3490	. . . . . . . . . . . 12 Poly $/\$ deg $/\$ coeff Poly $\$
145		ssrexv 3547	. . . . . . . . . . . . 13 Poly $/\$ deg $/\$ coeff Poly $\$ Poly $/\$ deg $/\$ coeff Poly $\$
146	83	cbvrexv 3069	. . . . . . . . . . . . 13 Poly $\$ Poly $\$
147	145, 146	syl6ib 226	. . . . . . . . . . . 12 Poly $/\$ deg $/\$ coeff Poly $\$ Poly $/\$ deg $/\$ coeff Poly $\$
148	144, 147	ax-mp 5	. . . . . . . . . . 11 Poly $/\$ deg $/\$ coeff Poly $\$
149	148	anim2i 569	. . . . . . . . . 10 $/\$ Poly $/\$ deg $/\$ coeff $/\$ Poly $\$
150	134, 149	sylbi 195	. . . . . . . . 9 Poly $/\$ deg $/\$ coeff $/\$ Poly $\$
151	132, 150	syl6bi 228	. . . . . . . 8 Poly $/\$ deg $/\$ coeff $/\$ Poly $\$
152	151	rexlimivw 2930	. . . . . . 7 Poly $/\$ deg $/\$ coeff $/\$ Poly $\$
153	152	impcom 430	. . . . . 6 $/\$ Poly $/\$ deg $/\$ coeff $/\$ Poly $\$
154	153	exlimiv 1707	. . . . 5 $/\$ Poly $/\$ deg $/\$ coeff $/\$ Poly $\$
155	131, 154	impbii 188	. . . 4 $/\$ Poly $\$ $/\$ Poly $/\$ deg $/\$ coeff
156		elaa 22577	. . . 4 $/\$ Poly $\$
157		eluniab 4241	. . . 4 Poly $/\$ deg $/\$ coeff $/\$ Poly $/\$ deg $/\$ coeff
158	155, 156, 157	3bitr4i 277	. . 3 Poly $/\$ deg $/\$ coeff
159	158	eqriv 2437	. 2 Poly $/\$ deg $/\$ coeff
160		aannenlem.a	. . . 4 Poly $/\$ deg $/\$ coeff
161	160	rnmpt 5234	. . 3 Poly $/\$ deg $/\$ coeff
162	161	unieqi 4239	. 2 Poly $/\$ deg $/\$ coeff
163	159, 162	eqtr4i 2473	1

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ wa 369 $/\$ w3a 972

wceq 1381

wex 1597

wcel 1802

cab 2426

wne 2636

wral 2791

wrex 2792

crab 2795 $\$ cdif 3455

cun 3456

wss 3458

c0 3767

csn 4010

cpr 4012

cuni 4230 class class class wbr 4433

cmpt 4491

wor 4785

crn 4986

wf 5570

cfv 5574 (class class class)co 6277

cfn 7514

csup 7898

cc 9488

cr 9489

cc0 9490

cxr 9625

clt 9626

cle 9627

cn0 10796

cz 10865

cfz 11676

cabs 13041

c0p 21942 Polycply 22447 coeffccoe 22449 degcdgr 22450

caa 22575

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1603 ax-4 1616 ax-5 1689 ax-6 1732 ax-7 1774 ax-8 1804 ax-9 1806 ax-10 1821 ax-11 1826 ax-12 1838 ax-13 1983 ax-ext 2419 ax-rep 4544 ax-sep 4554 ax-nul 4562 ax-pow 4611 ax-pr 4672 ax-un 6573 ax-inf2 8056 ax-cnex 9546 ax-resscn 9547 ax-1cn 9548 ax-icn 9549 ax-addcl 9550 ax-addrcl 9551 ax-mulcl 9552 ax-mulrcl 9553 ax-mulcom 9554 ax-addass 9555 ax-mulass 9556 ax-distr 9557 ax-i2m1 9558 ax-1ne0 9559 ax-1rid 9560 ax-rnegex 9561 ax-rrecex 9562 ax-cnre 9563 ax-pre-lttri 9564 ax-pre-lttrn 9565 ax-pre-ltadd 9566 ax-pre-mulgt0 9567 ax-pre-sup 9568 ax-addf 9569

This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 973 df-3an 974 df-tru 1384 df-fal 1387 df-ex 1598 df-nf 1602 df-sb 1725 df-eu 2270 df-mo 2271 df-clab 2427 df-cleq 2433 df-clel 2436 df-nfc 2591 df-ne 2638 df-nel 2639 df-ral 2796 df-rex 2797 df-reu 2798 df-rmo 2799 df-rab 2800 df-v 3095 df-sbc 3312 df-csb 3418 df-dif 3461 df-un 3463 df-in 3465 df-ss 3472 df-pss 3474 df-nul 3768 df-if 3923 df-pw 3995 df-sn 4011 df-pr 4013 df-tp 4015 df-op 4017 df-uni 4231 df-int 4268 df-iun 4313 df-br 4434 df-opab 4492 df-mpt 4493 df-tr 4527 df-eprel 4777 df-id 4781 df-po 4786 df-so 4787 df-fr 4824 df-se 4825 df-we 4826 df-ord 4867 df-on 4868 df-lim 4869 df-suc 4870 df-xp 4991 df-rel 4992 df-cnv 4993 df-co 4994 df-dm 4995 df-rn 4996 df-res 4997 df-ima 4998 df-iota 5537 df-fun 5576 df-fn 5577 df-f 5578 df-f1 5579 df-fo 5580 df-f1o 5581 df-fv 5582 df-isom 5583 df-riota 6238 df-ov 6280 df-oprab 6281 df-mpt2 6282 df-of 6521 df-om 6682 df-1st 6781 df-2nd 6782 df-recs 7040 df-rdg 7074 df-1o 7128 df-oadd 7132 df-er 7309 df-map 7420 df-pm 7421 df-en 7515 df-dom 7516 df-sdom 7517 df-fin 7518 df-sup 7899 df-oi 7933 df-card 8318 df-pnf 9628 df-mnf 9629 df-xr 9630 df-ltxr 9631 df-le 9632 df-sub 9807 df-neg 9808 df-div 10208 df-nn 10538 df-2 10595 df-3 10596 df-n0 10797 df-z 10866 df-uz 11086 df-rp 11225 df-fz 11677 df-fzo 11799 df-fl 11903 df-seq 12082 df-exp 12141 df-hash 12380 df-cj 12906 df-re 12907 df-im 12908 df-sqrt 13042 df-abs 13043 df-clim 13285 df-rlim 13286 df-sum 13483 df-0p 21943 df-ply 22451 df-coe 22453 df-dgr 22454 df-aa 22576

This theorem is referenced by: aannenlem3 22591

W3C validator