cdleme31sc - Mathbox for Norm Megill

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Theorem cdleme31sc 35672

Description: Part of proof of Lemma E in [Crawley] p. 113. (Contributed by NM, 31-Mar-2013.)

**Hypotheses**
Ref	Expression
cdleme31sc.c	$.\/$ $./\$ $.\/$ $.\/$ $./\$
cdleme31sc.x	$.\/$ $./\$ $.\/$ $.\/$ $./\$

**Assertion**
Ref	Expression
cdleme31sc

$.\/$ ,

$./\$ ,

(

)

(

)

**Proof of Theorem cdleme31sc**
Step	Hyp	Ref	Expression
1		nfcvd 2765	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$
2		oveq1 6657	. . . 4 $.\/$ $.\/$
3		oveq2 6658	. . . . . 6 $.\/$ $.\/$
4	3	oveq1d 6665	. . . . 5 $.\/$ $./\$ $.\/$ $./\$
5	4	oveq2d 6666	. . . 4 $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$
6	2, 5	oveq12d 6668	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$
7	1, 6	csbiegf 3557	. 2 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$
8		cdleme31sc.c	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$
9	8	csbeq2i 3993	. 2 $.\/$ $./\$ $.\/$ $.\/$ $./\$
10		cdleme31sc.x	. 2 $.\/$ $./\$ $.\/$ $.\/$ $./\$
11	7, 9, 10	3eqtr4g 2681	1

Colors of variables: wff setvar class

Syntax hints:

wi 4

wceq 1483

wcel 1990

csb 3533 (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-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-ov 6653

This theorem is referenced by: cdleme31snd 35674 cdleme31sdnN 35675 cdlemefr44 35713 cdlemefr45e 35716 cdleme48fv 35787 cdleme46fvaw 35789 cdleme48bw 35790 cdleme46fsvlpq 35793 cdlemeg46fvcl 35794 cdlemeg49le 35799 cdlemeg46fjgN 35809 cdlemeg46rjgN 35810 cdlemeg46fjv 35811 cdleme48d 35823 cdlemeg49lebilem 35827 cdleme50eq 35829 cdleme50f 35830 cdlemg2jlemOLDN 35881 cdlemg2klem 35883