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Theorem rexeqbi1dv 2571
 Description: Equality deduction for restricted existential quantifier. (Contributed by NM, 18-Mar-1997.)
Hypothesis
Ref Expression
raleqd.1
Assertion
Ref Expression
rexeqbi1dv
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rexeqbi1dv
StepHypRef Expression
1 rexeq 2563 . 2
2 raleqd.1 . . 3
32rexbidv 2381 . 2
41, 3bitrd 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1289  wrex 2360 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070 This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365 This theorem is referenced by:  reg2exmid  4352  reg3exmid  4395  exmidomni  6798  bj-nn0suc0  11845
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