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Theorem rexeqdv 2814
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 2808 . 2
31, 2syl 15 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wceq 1642  wrex 2615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620
This theorem is referenced by:  rexeqbidv  2820  rexeqbidva  2822  clos1basesucg  5884
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