dveeq2 - Intuitionistic Logic Explorer

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Theorem dveeq2 1736

Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.)

**Assertion**
Ref	Expression
dveeq2

**Proof of Theorem dveeq2**
Step	Hyp	Ref	Expression
1		ax-i12 1438	. . . . 5 $\/$ $\/$
2		orcom 679	. . . . . 6 $\/$ $\/$
3	2	orbi2i 711	. . . . 5 $\/$ $\/$ $\/$ $\/$
4	1, 3	mpbi 143	. . . 4 $\/$ $\/$
5		orass 716	. . . 4 $\/$ $\/$ $\/$ $\/$
6	4, 5	mpbir 144	. . 3 $\/$ $\/$
7		orel2 677	. . 3 $\/$ $\/$ $\/$
8	6, 7	mpi 15	. 2 $\/$
9		ax16 1734	. . 3
10		sp 1441	. . 3
11	9, 10	jaoi 668	. 2 $\/$
12	8, 11	syl 14	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 661

wal 1282

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467

This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686

This theorem is referenced by: nd5 1739 ax11v2 1741 dveeq1 1936