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Theorem rexeqdv 2656
 Description: Equality deduction for restricted existential quantifier. (Contributed by NM, 14-Jan-2007.)
Hypothesis
Ref Expression
raleq1d.1
Assertion
Ref Expression
rexeqdv
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rexeqdv
StepHypRef Expression
1 raleq1d.1 . 2
2 rexeq 2650 . 2
31, 2syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332  wrex 2433 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-cleq 2147  df-clel 2150  df-nfc 2285  df-rex 2438 This theorem is referenced by:  rexeqbidv  2662  rexeqbidva  2664  fnunirn  5708  cbvexfo  5727  fival  6903  genipv  7408  exfzdc  10117  zproddc  11453  infssuzex  11809  ennnfonelemrnh  12104  cnpfval  12542
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