cdlemefrs29cpre1 - Mathbox for Norm Megill

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Theorem cdlemefrs29cpre1 34036

Description: TODO: FIX COMMENT. (Contributed by NM, 29-Mar-2013.)

**Hypotheses**
Ref	Expression
cdlemefrs27.b
cdlemefrs27.l
cdlemefrs27.j	$.\/$
cdlemefrs27.m	$./\$
cdlemefrs27.a
cdlemefrs27.h
cdlemefrs27.eq
cdlemefrs27.nb	$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
cdlemefrs27.rnb	$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

**Assertion**
Ref	Expression
cdlemefrs29cpre1	$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Distinct variable groups:

$.\/$ ,

, $.\/$ $./\$ ,

Allowed substitution hints:

(

)

(

)

**Proof of Theorem cdlemefrs29cpre1**
Step	Hyp	Ref	Expression
1		cdlemefrs27.b	. . 3
2		cdlemefrs27.l	. . 3
3		cdlemefrs27.j	. . 3 $.\/$
4		cdlemefrs27.m	. . 3 $./\$
5		cdlemefrs27.a	. . 3
6		cdlemefrs27.h	. . 3
7		cdlemefrs27.eq	. . 3
8		cdlemefrs27.nb	. . 3 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
9		cdlemefrs27.rnb	. . 3 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
10	1, 2, 3, 4, 5, 6, 7, 8, 9	cdlemefrs29bpre1 34035	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
11		simp11 1060	. . . . 5 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
12		simp2rl 1099	. . . . . 6 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
13	1, 5	atbase 32926	. . . . . 6
14	12, 13	syl 17	. . . . 5 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
15		simp2rr 1100	. . . . 5 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
16	1, 2, 3, 4, 5, 6	lhpmcvr2 33660	. . . . 5 $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
17	11, 14, 15, 16	syl12anc 1290	. . . 4 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
18		simpl3 1035	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
19	7	pm5.32ri 650	. . . . . . . . . 10 $/\$ $/\$
20	19	baibr 920	. . . . . . . . 9 $/\$
21	18, 20	syl 17	. . . . . . . 8 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
22		simp2r 1057	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
23		eqid 2471	. . . . . . . . . . . . . 14
24	2, 4, 23, 5, 6	lhpmat 33666	. . . . . . . . . . . . 13 $/\$ $/\$ $/\$ $./\$
25	11, 22, 24	syl2anc 673	. . . . . . . . . . . 12 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $./\$
26	25	adantr 472	. . . . . . . . . . 11 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $./\$
27	26	oveq2d 6324	. . . . . . . . . 10 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$
28		simp11l 1141	. . . . . . . . . . . 12 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
29		hlol 32998	. . . . . . . . . . . 12
30	28, 29	syl 17	. . . . . . . . . . 11 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
31	1, 5	atbase 32926	. . . . . . . . . . 11
32	1, 3, 23	olj01 32862	. . . . . . . . . . 11 $/\$ $.\/$
33	30, 31, 32	syl2an 485	. . . . . . . . . 10 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$
34	27, 33	eqtrd 2505	. . . . . . . . 9 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
35	34	eqeq1d 2473	. . . . . . . 8 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
36	35	anbi2d 718	. . . . . . . 8 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$
37	21, 35, 36	3bitr4d 293	. . . . . . 7 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $.\/$ $./\$
38	37	anbi2d 718	. . . . . 6 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$
39		anass 661	. . . . . 6 $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$
40	38, 39	syl6bbr 271	. . . . 5 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$
41	40	rexbidva 2889	. . . 4 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$
42	17, 41	mpbid 215	. . 3 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$
43		reusv1 4601	. . 3 $/\$ $/\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
44	42, 43	syl 17	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
45	10, 44	mpbird 240	1 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wb 189 $/\$ wa 376 $/\$ w3a 1007

wceq 1452

wcel 1904

wne 2641

wral 2756

wrex 2757

wreu 2758

csb 3349 class class class wbr 4395

cfv 5589 (class class class)co 6308

cbs 15199

cple 15275

cjn 16267

cmee 16268

cp0 16361

col 32811

catm 32900

chlt 32987

clh 33620

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-rep 4508 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 ax-un 6602

This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-reu 2763 df-rmo 2764 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-iun 4271 df-br 4396 df-opab 4455 df-mpt 4456 df-id 4754 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-riota 6270 df-ov 6311 df-oprab 6312 df-preset 16251 df-poset 16269 df-plt 16282 df-lub 16298 df-glb 16299 df-join 16300 df-meet 16301 df-p0 16363 df-p1 16364 df-lat 16370 df-clat 16432 df-oposet 32813 df-ol 32815 df-oml 32816 df-covers 32903 df-ats 32904 df-atl 32935 df-cvlat 32959 df-hlat 32988 df-lhyp 33624

This theorem is referenced by: cdlemefrs29clN 34037 cdlemefrs32fva 34038 cdlemefs29cpre1N 34056

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