cdleme31fv - Mathbox for Norm Megill

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Theorem cdleme31fv 35678

Description: Part of proof of Lemma E in [Crawley] p. 113. (Contributed by NM, 10-Feb-2013.)

**Assertion**
Ref	Expression
cdleme31fv	$/\$

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**Proof of Theorem cdleme31fv**
Step	Hyp	Ref	Expression
1		cdleme31.c	. . . 4 $/\$ $.\/$ $./\$ $.\/$ $./\$
2		riotaex 6615	. . . 4 $/\$ $.\/$ $./\$ $.\/$ $./\$
3	1, 2	eqeltri 2697	. . 3
4		ifexg 4157	. . 3 $/\$ $/\$
5	3, 4	mpan 706	. 2 $/\$
6		breq1 4656	. . . . . 6
7	6	notbid 308	. . . . 5
8	7	anbi2d 740	. . . 4 $/\$ $/\$
9		oveq1 6657	. . . . . . . . . . 11 $./\$ $./\$
10	9	oveq2d 6666	. . . . . . . . . 10 $.\/$ $./\$ $.\/$ $./\$
11		id 22	. . . . . . . . . 10
12	10, 11	eqeq12d 2637	. . . . . . . . 9 $.\/$ $./\$ $.\/$ $./\$
13	12	anbi2d 740	. . . . . . . 8 $/\$ $.\/$ $./\$ $/\$ $.\/$ $./\$
14	9	oveq2d 6666	. . . . . . . . 9 $.\/$ $./\$ $.\/$ $./\$
15	14	eqeq2d 2632	. . . . . . . 8 $.\/$ $./\$ $.\/$ $./\$
16	13, 15	imbi12d 334	. . . . . . 7 $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
17	16	ralbidv 2986	. . . . . 6 $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
18	17	riotabidv 6613	. . . . 5 $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
19		cdleme31.o	. . . . 5 $/\$ $.\/$ $./\$ $.\/$ $./\$
20	18, 19, 1	3eqtr4g 2681	. . . 4
21	8, 20, 11	ifbieq12d 4113	. . 3 $/\$ $/\$
22		cdleme31.f	. . 3 $/\$
23	21, 22	fvmptg 6280	. 2 $/\$ $/\$ $/\$
24	5, 23	mpdan 702	1 $/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4 $/\$ wa 384

wceq 1483

wcel 1990

wne 2794

wral 2912

cvv 3200

cif 4086 class class class wbr 4653

cmpt 4729

cfv 5888

crio 6610 (class class class)co 6650

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-riota 6611 df-ov 6653

This theorem is referenced by: cdleme31fv1 35679