4atex2-0cOLDN - Mathbox for Norm Megill

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Theorem 4atex2-0cOLDN 35366

Description: Same as 4atex2 35363 except that

and

are zero. TODO: do we need this one or 4atex2-0aOLDN 35364 or 4atex2-0bOLDN 35365? (Contributed by NM, 27-May-2013.) (New usage is discouraged.)

**Assertion**
Ref	Expression
4atex2-0cOLDN	$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $.\/$

$.\/$ ,

**Proof of Theorem 4atex2-0cOLDN**
Step	Hyp	Ref	Expression
1		simp21l 1178	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$
2		simp21r 1179	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$
3		simp23 1096	. . . 4 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$
4	3	oveq1d 6665	. . 3 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $.\/$
5		simp32 1098	. . . 4 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$
6	5	oveq1d 6665	. . 3 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $.\/$
7	4, 6	eqtr4d 2659	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $.\/$
8		breq1 4656	. . . . 5
9	8	notbid 308	. . . 4
10		oveq2 6658	. . . . 5 $.\/$ $.\/$
11		oveq2 6658	. . . . 5 $.\/$ $.\/$
12	10, 11	eqeq12d 2637	. . . 4 $.\/$ $.\/$ $.\/$ $.\/$
13	9, 12	anbi12d 747	. . 3 $/\$ $.\/$ $.\/$ $/\$ $.\/$ $.\/$
14	13	rspcev 3309	. 2 $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $.\/$
15	1, 2, 7, 14	syl12anc 1324	1 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $.\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4 $/\$ wa 384 $/\$ w3a 1037

wceq 1483

wcel 1990

wne 2794

wrex 2913 class class class wbr 4653

cfv 5888 (class class class)co 6650

cple 15948

cjn 16944

cp0 17037

catm 34550

chlt 34637

clh 35270

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-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: (None)