cdleme31so - Mathbox for Norm Megill

	Mathbox for Norm Megill		< Previous Next > Nearby theorems
Mirrors > Home > MPE Home > Th. List > Mathboxes > cdleme31so		Structured version Visualization version Unicode version

Theorem cdleme31so 35667

Description: Part of proof of Lemma E in [Crawley] p. 113. (Contributed by NM, 25-Feb-2013.)

**Hypotheses**
Ref	Expression
cdleme31so.o	$/\$ $.\/$ $./\$ $.\/$ $./\$
cdleme31so.c	$/\$ $.\/$ $./\$ $.\/$ $./\$

**Assertion**
Ref	Expression
cdleme31so

, $.\/$

, $./\$

(

)

(

)

(

) $.\/$ (

)

(

) $./\$ (

)

(

)

(

)

(

)

**Proof of Theorem cdleme31so**
Step	Hyp	Ref	Expression
1		nfcvd 2765	. . 3 $/\$ $.\/$ $./\$ $.\/$ $./\$
2		oveq1 6657	. . . . . . . . 9 $./\$ $./\$
3	2	oveq2d 6666	. . . . . . . 8 $.\/$ $./\$ $.\/$ $./\$
4		id 22	. . . . . . . 8
5	3, 4	eqeq12d 2637	. . . . . . 7 $.\/$ $./\$ $.\/$ $./\$
6	5	anbi2d 740	. . . . . 6 $/\$ $.\/$ $./\$ $/\$ $.\/$ $./\$
7	2	oveq2d 6666	. . . . . . 7 $.\/$ $./\$ $.\/$ $./\$
8	7	eqeq2d 2632	. . . . . 6 $.\/$ $./\$ $.\/$ $./\$
9	6, 8	imbi12d 334	. . . . 5 $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
10	9	ralbidv 2986	. . . 4 $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
11	10	riotabidv 6613	. . 3 $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
12	1, 11	csbiegf 3557	. 2 $/\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $.\/$ $./\$ $.\/$ $./\$
13		cdleme31so.o	. . 3 $/\$ $.\/$ $./\$ $.\/$ $./\$
14	13	csbeq2i 3993	. 2 $/\$ $.\/$ $./\$ $.\/$ $./\$
15		cdleme31so.c	. 2 $/\$ $.\/$ $./\$ $.\/$ $./\$
16	12, 14, 15	3eqtr4g 2681	1

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4 $/\$ wa 384

wceq 1483

wcel 1990

wral 2912

csb 3533 class class class wbr 4653

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

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-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-csb 3534 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-iota 5851 df-fv 5896 df-riota 6611 df-ov 6653

This theorem is referenced by: cdleme31fv1s 35680 cdlemefrs32fva 35688 cdleme32fva 35725