dveeq2 - Intuitionistic Logic Explorer

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Theorem dveeq2 1769

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 1468	. . . . 5 $\/$ $\/$
2		orcom 700	. . . . . 6 $\/$ $\/$
3	2	orbi2i 734	. . . . 5 $\/$ $\/$ $\/$ $\/$
4	1, 3	mpbi 144	. . . 4 $\/$ $\/$
5		orass 739	. . . 4 $\/$ $\/$ $\/$ $\/$
6	4, 5	mpbir 145	. . 3 $\/$ $\/$
7		orel2 698	. . 3 $\/$ $\/$ $\/$
8	6, 7	mpi 15	. 2 $\/$
9		ax16 1767	. . 3
10		sp 1471	. . 3
11	9, 10	jaoi 688	. 2 $\/$
12	8, 11	syl 14	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 680

wal 1312

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 587 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497

This theorem depends on definitions: df-bi 116 df-nf 1420 df-sb 1719

This theorem is referenced by: nd5 1772 ax11v2 1774 dveeq1 1970