dihglbcpreN - Mathbox for Norm Megill

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Theorem dihglbcpreN 34914

Description: Isomorphism H of a lattice glb when the glb is not under the fiducial hyperplane

. (Contributed by NM, 20-Mar-2014.) (New usage is discouraged.)

**Hypotheses**
Ref	Expression
dihglbc.b
dihglbc.g
dihglbc.h
dihglbc.i
dihglbc.l
dihglbcpre.j	$.\/$
dihglbcpre.m	$./\$
dihglbcpre.a
dihglbcpre.p
dihglbcpre.t
dihglbcpre.r
dihglbcpre.e
dihglbcpre.f

**Assertion**
Ref	Expression
dihglbcpreN	$/\$ $/\$ $/\$ $/\$

Distinct variable groups:

, $./\$

, $.\/$

Allowed substitution hints:

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

) $.\/$ (

) $./\$ (

)

Proof of Theorem dihglbcpreN Dummy variables

are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		dihglbc.h	. . . 4
2		dihglbc.i	. . . 4
3	1, 2	dihvalrel 34893	. . 3 $/\$
4	3	3ad2ant1 1035	. 2 $/\$ $/\$ $/\$ $/\$
5		simp2r 1041	. . . . . 6 $/\$ $/\$ $/\$ $/\$
6		n0 3753	. . . . . 6
7	5, 6	sylib 201	. . . . 5 $/\$ $/\$ $/\$ $/\$
8		simpr 467	. . . . . . . 8 $/\$ $/\$ $/\$ $/\$ $/\$
9		simpl1 1017	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
10	1, 2	dihvalrel 34893	. . . . . . . . 9 $/\$
11	9, 10	syl 17	. . . . . . . 8 $/\$ $/\$ $/\$ $/\$ $/\$
12	8, 11	jca 539	. . . . . . 7 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
13	12	ex 440	. . . . . 6 $/\$ $/\$ $/\$ $/\$ $/\$
14	13	eximdv 1775	. . . . 5 $/\$ $/\$ $/\$ $/\$ $/\$
15	7, 14	mpd 15	. . . 4 $/\$ $/\$ $/\$ $/\$ $/\$
16		df-rex 2755	. . . 4 $/\$
17	15, 16	sylibr 217	. . 3 $/\$ $/\$ $/\$ $/\$
18		reliin 4977	. . 3
19	17, 18	syl 17	. 2 $/\$ $/\$ $/\$ $/\$
20		id 22	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
21		simp1 1014	. . . . 5 $/\$ $/\$ $/\$ $/\$ $/\$
22		simp1l 1038	. . . . . . 7 $/\$ $/\$ $/\$ $/\$
23		hlclat 32970	. . . . . . 7
24	22, 23	syl 17	. . . . . 6 $/\$ $/\$ $/\$ $/\$
25		simp2l 1040	. . . . . 6 $/\$ $/\$ $/\$ $/\$
26		dihglbc.b	. . . . . . 7
27		dihglbc.g	. . . . . . 7
28	26, 27	clatglbcl 16415	. . . . . 6 $/\$
29	24, 25, 28	syl2anc 671	. . . . 5 $/\$ $/\$ $/\$ $/\$
30		simp3 1016	. . . . 5 $/\$ $/\$ $/\$ $/\$
31		dihglbc.l	. . . . . 6
32		dihglbcpre.j	. . . . . 6 $.\/$
33		dihglbcpre.m	. . . . . 6 $./\$
34		dihglbcpre.a	. . . . . 6
35	26, 31, 32, 33, 34, 1	lhpmcvr2 33635	. . . . 5 $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
36	21, 29, 30, 35	syl12anc 1274	. . . 4 $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
37		simpl1 1017	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
38	29	adantr 471	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
39		simpl3 1019	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
40		simpr 467	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$
41		dihglbcpre.p	. . . . . . . . . 10
42		dihglbcpre.t	. . . . . . . . . 10
43		dihglbcpre.r	. . . . . . . . . 10
44		dihglbcpre.e	. . . . . . . . . 10
45		dihglbcpre.f	. . . . . . . . . 10
46		vex 3060	. . . . . . . . . 10
47		vex 3060	. . . . . . . . . 10
48	26, 31, 32, 33, 34, 1, 41, 42, 43, 44, 2, 45, 46, 47	dihopelvalc 34863	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
49	37, 38, 39, 40, 48	syl121anc 1281	. . . . . . . 8 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
50		simpl2r 1068	. . . . . . . . . . 11 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
51		r19.28zv 3876	. . . . . . . . . . 11 $/\$ $/\$ $/\$ $/\$
52	50, 51	syl 17	. . . . . . . . . 10 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$
53		simp11 1044	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
54		simp12l 1127	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
55		simp3 1016	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
56	54, 55	sseldd 3445	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
57		simp13 1046	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
58		simp11l 1125	. . . . . . . . . . . . . . . . 17 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
59	58, 23	syl 17	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
60	26, 31, 27	clatglble 16426	. . . . . . . . . . . . . . . 16 $/\$ $/\$
61	59, 54, 55, 60	syl3anc 1276	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
62		hllat 32975	. . . . . . . . . . . . . . . . 17
63	58, 62	syl 17	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
64	29	3ad2ant1 1035	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
65		simp11r 1126	. . . . . . . . . . . . . . . . 17 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
66	26, 1	lhpbase 33609	. . . . . . . . . . . . . . . . 17
67	65, 66	syl 17	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
68	26, 31	lattr 16357	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$
69	63, 64, 56, 67, 68	syl13anc 1278	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
70	61, 69	mpand 686	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
71	57, 70	mtod 182	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
72		simp2l 1040	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
73		simp2ll 1081	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
74	26, 34	atbase 32901	. . . . . . . . . . . . . . . . 17
75	73, 74	syl 17	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
76	26, 33	latmcl 16353	. . . . . . . . . . . . . . . . . . 19 $/\$ $/\$ $./\$
77	63, 64, 67, 76	syl3anc 1276	. . . . . . . . . . . . . . . . . 18 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $./\$
78	26, 31, 32	latlej1 16361	. . . . . . . . . . . . . . . . . 18 $/\$ $/\$ $./\$ $.\/$ $./\$
79	63, 75, 77, 78	syl3anc 1276	. . . . . . . . . . . . . . . . 17 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $.\/$ $./\$
80		simp2r 1041	. . . . . . . . . . . . . . . . 17 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $.\/$ $./\$
81	79, 80	breqtrd 4443	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
82	26, 31, 63, 75, 64, 56, 81, 61	lattrd 16359	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
83	26, 31, 32, 33, 34	atmod3i1 33475	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $./\$ $.\/$
84	58, 73, 56, 67, 82, 83	syl131anc 1289	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $./\$ $.\/$
85		eqid 2462	. . . . . . . . . . . . . . . . 17
86	31, 32, 85, 34, 1	lhpjat2 33632	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $.\/$
87	53, 72, 86	syl2anc 671	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $.\/$
88	87	oveq2d 6336	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $./\$ $.\/$ $./\$
89		hlol 32973	. . . . . . . . . . . . . . . 16
90	58, 89	syl 17	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
91	26, 33, 85	olm11 32839	. . . . . . . . . . . . . . 15 $/\$ $./\$
92	90, 56, 91	syl2anc 671	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $./\$
93	84, 88, 92	3eqtrd 2500	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $.\/$ $./\$
94	26, 31, 32, 33, 34, 1, 41, 42, 43, 44, 2, 45, 46, 47	dihopelvalc 34863	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
95	53, 56, 71, 72, 93, 94	syl122anc 1285	. . . . . . . . . . . 12 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $/\$
96	95	3expa 1215	. . . . . . . . . . 11 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $/\$
97	96	ralbidva 2836	. . . . . . . . . 10 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
98		simp11l 1125	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
99	98, 23	syl 17	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
100		simp11 1044	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $/\$
101		simp3l 1042	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
102		simp3r 1043	. . . . . . . . . . . . . . . . 17 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
103	31, 34, 1, 41	lhpocnel2 33630	. . . . . . . . . . . . . . . . . . 19 $/\$ $/\$
104	100, 103	syl 17	. . . . . . . . . . . . . . . . . 18 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $/\$
105		simp2l 1040	. . . . . . . . . . . . . . . . . 18 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $/\$
106	31, 34, 1, 42, 45	ltrniotacl 34192	. . . . . . . . . . . . . . . . . 18 $/\$ $/\$ $/\$ $/\$ $/\$
107	100, 104, 105, 106	syl3anc 1276	. . . . . . . . . . . . . . . . 17 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
108	1, 42, 44	tendocl 34380	. . . . . . . . . . . . . . . . 17 $/\$ $/\$ $/\$
109	100, 102, 107, 108	syl3anc 1276	. . . . . . . . . . . . . . . 16 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
110	1, 42	ltrncnv 33757	. . . . . . . . . . . . . . . 16 $/\$ $/\$
111	100, 109, 110	syl2anc 671	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
112	1, 42	ltrnco 34332	. . . . . . . . . . . . . . 15 $/\$ $/\$ $/\$
113	100, 101, 111, 112	syl3anc 1276	. . . . . . . . . . . . . 14 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
114	26, 1, 42, 43	trlcl 33776	. . . . . . . . . . . . . 14 $/\$ $/\$
115	100, 113, 114	syl2anc 671	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
116		simp12l 1127	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
117	26, 31, 27	clatleglb 16427	. . . . . . . . . . . . 13 $/\$ $/\$
118	99, 115, 116, 117	syl3anc 1276	. . . . . . . . . . . 12 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
119	118	3expa 1215	. . . . . . . . . . 11 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
120	119	pm5.32da 651	. . . . . . . . . 10 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$
121	52, 97, 120	3bitr4rd 294	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
122		opex 4681	. . . . . . . . . 10
123		eliin 4298	. . . . . . . . . 10
124	122, 123	ax-mp 5	. . . . . . . . 9
125	121, 124	syl6bbr 271	. . . . . . . 8 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$
126	49, 125	bitrd 261	. . . . . . 7 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
127	126	exp44 622	. . . . . 6 $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
128	127	imp4a 598	. . . . 5 $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
129	128	rexlimdv 2889	. . . 4 $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
130	36, 129	mpd 15	. . 3 $/\$ $/\$ $/\$ $/\$
131	130	eqrelrdv2 4956	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
132	4, 19, 20, 131	syl21anc 1275	1 $/\$ $/\$ $/\$ $/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wb 189 $/\$ wa 375 $/\$ w3a 991

wceq 1455

wex 1674

wcel 1898

wne 2633

wral 2749

wrex 2750

cvv 3057

wss 3416

c0 3743

cop 3986

ciin 4293 class class class wbr 4418

ccnv 4855

ccom 4860

wrel 4861

cfv 5605

crio 6281 (class class class)co 6320

cbs 15176

cple 15252

coc 15253

cglb 16243

cjn 16244

cmee 16245

cp1 16339

clat 16346

ccla 16408

col 32786

catm 32875

chlt 32962

clh 33595

cltrn 33712

ctrl 33770

ctendo 34365

cdih 34842

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-rep 4531 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-un 6615 ax-cnex 9626 ax-resscn 9627 ax-1cn 9628 ax-icn 9629 ax-addcl 9630 ax-addrcl 9631 ax-mulcl 9632 ax-mulrcl 9633 ax-mulcom 9634 ax-addass 9635 ax-mulass 9636 ax-distr 9637 ax-i2m1 9638 ax-1ne0 9639 ax-1rid 9640 ax-rnegex 9641 ax-rrecex 9642 ax-cnre 9643 ax-pre-lttri 9644 ax-pre-lttrn 9645 ax-pre-ltadd 9646 ax-pre-mulgt0 9647 ax-riotaBAD 32571

This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1458 df-fal 1461 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-nel 2636 df-ral 2754 df-rex 2755 df-reu 2756 df-rmo 2757 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-pss 3432 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-tp 3985 df-op 3987 df-uni 4213 df-int 4249 df-iun 4294 df-iin 4295 df-br 4419 df-opab 4478 df-mpt 4479 df-tr 4514 df-eprel 4767 df-id 4771 df-po 4777 df-so 4778 df-fr 4815 df-we 4817 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-pred 5403 df-ord 5449 df-on 5450 df-lim 5451 df-suc 5452 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-riota 6282 df-ov 6323 df-oprab 6324 df-mpt2 6325 df-om 6725 df-1st 6825 df-2nd 6826 df-tpos 7004 df-undef 7051 df-wrecs 7059 df-recs 7121 df-rdg 7159 df-1o 7213 df-oadd 7217 df-er 7394 df-map 7505 df-en 7601 df-dom 7602 df-sdom 7603 df-fin 7604 df-pnf 9708 df-mnf 9709 df-xr 9710 df-ltxr 9711 df-le 9712 df-sub 9893 df-neg 9894 df-nn 10643 df-2 10701 df-3 10702 df-4 10703 df-5 10704 df-6 10705 df-n0 10904 df-z 10972 df-uz 11194 df-fz 11820 df-struct 15178 df-ndx 15179 df-slot 15180 df-base 15181 df-sets 15182 df-ress 15183 df-plusg 15258 df-mulr 15259 df-sca 15261 df-vsca 15262 df-0g 15395 df-preset 16228 df-poset 16246 df-plt 16259 df-lub 16275 df-glb 16276 df-join 16277 df-meet 16278 df-p0 16340 df-p1 16341 df-lat 16347 df-clat 16409 df-mgm 16543 df-sgrp 16582 df-mnd 16592 df-submnd 16638 df-grp 16728 df-minusg 16729 df-sbg 16730 df-subg 16869 df-cntz 17026 df-lsm 17343 df-cmn 17487 df-abl 17488 df-mgp 17779 df-ur 17791 df-ring 17837 df-oppr 17906 df-dvdsr 17924 df-unit 17925 df-invr 17955 df-dvr 17966 df-drng 18032 df-lmod 18148 df-lss 18211 df-lsp 18250 df-lvec 18381 df-oposet 32788 df-ol 32790 df-oml 32791 df-covers 32878 df-ats 32879 df-atl 32910 df-cvlat 32934 df-hlat 32963 df-llines 33109 df-lplanes 33110 df-lvols 33111 df-lines 33112 df-psubsp 33114 df-pmap 33115 df-padd 33407 df-lhyp 33599 df-laut 33600 df-ldil 33715 df-ltrn 33716 df-trl 33771 df-tendo 34368 df-edring 34370 df-disoa 34643 df-dvech 34693 df-dib 34753 df-dic 34787 df-dih 34843

This theorem is referenced by: dihglbcN 34915

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