cdleme31se - Mathbox for Norm Megill

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Theorem cdleme31se 35670

Description: Part of proof of Lemma D in [Crawley] p. 113. (Contributed by NM, 26-Feb-2013.)

**Hypotheses**
Ref	Expression
cdleme31se.e	$.\/$ $./\$ $.\/$ $.\/$ $./\$
cdleme31se.y	$.\/$ $./\$ $.\/$ $.\/$ $./\$

**Assertion**
Ref	Expression
cdleme31se

$.\/$ ,

$./\$ ,

(

)

(

)

**Proof of Theorem cdleme31se**
Step	Hyp	Ref	Expression
1		nfcvd 2765	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$
2		oveq1 6657	. . . . . 6 $.\/$ $.\/$
3	2	oveq1d 6665	. . . . 5 $.\/$ $./\$ $.\/$ $./\$
4	3	oveq2d 6666	. . . 4 $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$
5	4	oveq2d 6666	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$
6	1, 5	csbiegf 3557	. 2 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$
7		cdleme31se.e	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$
8	7	csbeq2i 3993	. 2 $.\/$ $./\$ $.\/$ $.\/$ $./\$
9		cdleme31se.y	. 2 $.\/$ $./\$ $.\/$ $.\/$ $./\$
10	6, 8, 9	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: cdleme31sde 35673 cdleme31sn1c 35676