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Theorem rexeqbid 3067
Description: Equality deduction for restricted existential quantifier. (Contributed by Thierry Arnoux, 8-Mar-2017.)
Hypotheses
Ref Expression
raleqbid.0
raleqbid.1
raleqbid.2
raleqbid.3
raleqbid.4
Assertion
Ref Expression
rexeqbid

Proof of Theorem rexeqbid
StepHypRef Expression
1 raleqbid.3 . . 3
2 raleqbid.1 . . . 4
3 raleqbid.2 . . . 4
42, 3rexeqf 3051 . . 3
51, 4syl 16 . 2
6 raleqbid.0 . . 3
7 raleqbid.4 . . 3
86, 7rexbid 2967 . 2
95, 8bitrd 253 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  F/wnf 1616  F/_wnfc 2605  E.wrex 2808
This theorem is referenced by:  iuneq12df  4354
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813
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