cdlemk41 - Mathbox for Norm Megill

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Theorem cdlemk41 36208

Description: Part of proof of Lemma K of [Crawley] p. 118. TODO: fix comment. (Contributed by NM, 19-Jul-2013.)

**Hypothesis**
Ref	Expression
cdlemk41.y	$.\/$ $./\$ $.\/$

**Assertion**
Ref	Expression
cdlemk41	$.\/$ $./\$ $.\/$

Distinct variable groups: $./\$ ,

$.\/$ ,

(

)

(

)

(

)

(

) $.\/$ (

) $./\$ (

)

(

)

(

)

**Proof of Theorem cdlemk41**
Step	Hyp	Ref	Expression
1		nfcvd 2765	. 2 $.\/$ $./\$ $.\/$
2		cdlemk41.y	. . 3 $.\/$ $./\$ $.\/$
3		fveq2 6191	. . . . 5
4	3	oveq2d 6666	. . . 4 $.\/$ $.\/$
5		coeq1 5279	. . . . . 6
6	5	fveq2d 6195	. . . . 5
7	6	oveq2d 6666	. . . 4 $.\/$ $.\/$
8	4, 7	oveq12d 6668	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$
9	2, 8	syl5eq 2668	. 2 $.\/$ $./\$ $.\/$
10	1, 9	csbiegf 3557	1 $.\/$ $./\$ $.\/$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wceq 1483

wcel 1990

csb 3533

ccnv 5113

ccom 5118

cfv 5888 (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-opab 4713 df-co 5123 df-iota 5851 df-fv 5896 df-ov 6653

This theorem is referenced by: cdlemkid2 36212 cdlemkfid3N 36213 cdlemky 36214 cdlemk42yN 36232