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Theorem dveeq2 1788
 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 1486 . . . . 5
2 orcom 718 . . . . . 6
32orbi2i 752 . . . . 5
41, 3mpbi 144 . . . 4
5 orass 757 . . . 4
64, 5mpbir 145 . . 3
7 orel2 716 . . 3
86, 7mpi 15 . 2
9 ax16 1786 . . 3
10 sp 1489 . . 3
119, 10jaoi 706 . 2
128, 11syl 14 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 698  wal 1330 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 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737 This theorem is referenced by:  nd5  1791  ax11v2  1793  dveeq1  1995
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