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Theorem rexeqbid 2986
 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 2970 . . 3
51, 4syl 17 . 2
6 raleqbid.0 . . 3
7 raleqbid.4 . . 3
86, 7rexbid 2891 . 2
95, 8bitrd 261 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wceq 1452  wnf 1675  wnfc 2599  wrex 2757 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762 This theorem is referenced by:  iuneq12df  4293
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