dveeq2 - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > dveeq2		Unicode version

Theorem dveeq2 1826

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		ax12or 1519	. . . . 5 $\/$ $\/$
2		orcom 729	. . . . . 6 $\/$ $\/$
3	2	orbi2i 763	. . . . 5 $\/$ $\/$ $\/$ $\/$
4	1, 3	mpbi 145	. . . 4 $\/$ $\/$
5		orass 768	. . . 4 $\/$ $\/$ $\/$ $\/$
6	4, 5	mpbir 146	. . 3 $\/$ $\/$
7		orel2 727	. . 3 $\/$ $\/$ $\/$
8	6, 7	mpi 15	. 2 $\/$
9		ax16 1824	. . 3
10		sp 1522	. . 3
11	9, 10	jaoi 717	. 2 $\/$
12	8, 11	syl 14	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 709

wal 1362

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545

This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774

This theorem is referenced by: nd5 1829 ax11v2 1831 dveeq1 2035