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Theorem rexeqbidv 2637
 Description: Equality deduction for restricted universal quantifier. (Contributed by NM, 6-Nov-2007.)
Hypotheses
Ref Expression
raleqbidv.1
raleqbidv.2
Assertion
Ref Expression
rexeqbidv
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rexeqbidv
StepHypRef Expression
1 raleqbidv.1 . . 3
21rexeqdv 2631 . 2
3 raleqbidv.2 . . 3
43rexbidv 2436 . 2
52, 4bitrd 187 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1331  wrex 2415 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420 This theorem is referenced by:  supeq123d  6871
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