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Theorem rexeqf 2893
 Description: Equality theorem for restricted existential quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 9-Oct-2003.) (Revised by Andrew Salmon, 11-Jul-2011.)
Hypotheses
Ref Expression
raleq1f.1
raleq1f.2
Assertion
Ref Expression
rexeqf

Proof of Theorem rexeqf
StepHypRef Expression
1 raleq1f.1 . . . 4
2 raleq1f.2 . . . 4
31, 2nfeq 2578 . . 3
4 eleq2 2496 . . . 4
54anbi1d 686 . . 3
63, 5exbid 1789 . 2
7 df-rex 2703 . 2
8 df-rex 2703 . 2
96, 7, 83bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  wnfc 2558  wrex 2698 This theorem is referenced by:  rexeq  2897  zfrep6  5960  rexeqbid  23956  iuneq12daf  23999  indexa  26426 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703
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