dveeq2 - Intuitionistic Logic Explorer

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Theorem dveeq2 1787

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 1485	. . . . 5 $\/$ $\/$
2		orcom 717	. . . . . 6 $\/$ $\/$
3	2	orbi2i 751	. . . . 5 $\/$ $\/$ $\/$ $\/$
4	1, 3	mpbi 144	. . . 4 $\/$ $\/$
5		orass 756	. . . 4 $\/$ $\/$ $\/$ $\/$
6	4, 5	mpbir 145	. . 3 $\/$ $\/$
7		orel2 715	. . 3 $\/$ $\/$ $\/$
8	6, 7	mpi 15	. 2 $\/$
9		ax16 1785	. . 3
10		sp 1488	. . 3
11	9, 10	jaoi 705	. 2 $\/$
12	8, 11	syl 14	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 697

wal 1329

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514

This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736

This theorem is referenced by: nd5 1790 ax11v2 1792 dveeq1 1992