3dim1lem5 - Mathbox for Norm Megill

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Theorem 3dim1lem5 34752

Description: Lemma for 3dim1 34753. (Contributed by NM, 26-Jul-2012.)

**Assertion**
Ref	Expression
3dim1lem5	$/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$

$.\/$ ,

(

)

**Proof of Theorem 3dim1lem5**
Step	Hyp	Ref	Expression
1		neeq2 2857	. . 3
2		oveq2 6658	. . . . 5 $.\/$ $.\/$
3	2	breq2d 4665	. . . 4 $.\/$ $.\/$
4	3	notbid 308	. . 3 $.\/$ $.\/$
5	2	oveq1d 6665	. . . . 5 $.\/$ $.\/$ $.\/$ $.\/$
6	5	breq2d 4665	. . . 4 $.\/$ $.\/$ $.\/$ $.\/$
7	6	notbid 308	. . 3 $.\/$ $.\/$ $.\/$ $.\/$
8	1, 4, 7	3anbi123d 1399	. 2 $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$
9		breq1 4656	. . . 4 $.\/$ $.\/$
10	9	notbid 308	. . 3 $.\/$ $.\/$
11		oveq2 6658	. . . . 5 $.\/$ $.\/$ $.\/$ $.\/$
12	11	breq2d 4665	. . . 4 $.\/$ $.\/$ $.\/$ $.\/$
13	12	notbid 308	. . 3 $.\/$ $.\/$ $.\/$ $.\/$
14	10, 13	3anbi23d 1402	. 2 $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$
15		breq1 4656	. . . 4 $.\/$ $.\/$ $.\/$ $.\/$
16	15	notbid 308	. . 3 $.\/$ $.\/$ $.\/$ $.\/$
17	16	3anbi3d 1405	. 2 $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$
18	8, 14, 17	rspc3ev 3326	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

catm 34550

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-ne 2795 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: 3dim1 34753