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Theorem dveeq2 1693
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.)
Assertion
Ref Expression
dveeq2
Distinct variable group:   ,

Proof of Theorem dveeq2
StepHypRef Expression
1 ax-i12 1395 . . . . 5
2 orcom 646 . . . . . 6
32orbi2i 678 . . . . 5
41, 3mpbi 133 . . . 4
5 orass 683 . . . 4
64, 5mpbir 134 . . 3
7 orel2 644 . . 3
86, 7mpi 15 . 2
9 ax16 1691 . . 3
10 sp 1398 . . 3
119, 10jaoi 635 . 2
128, 11syl 14 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wo 628  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  nd5  1696  ax11v2  1698  dveeq1  1892
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