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Theorem rexeqf 2627
 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 2290 . . 3
4 eleq2 2204 . . . 4
54anbi1d 461 . . 3
63, 5exbid 1596 . 2
7 df-rex 2423 . 2
8 df-rex 2423 . 2
96, 7, 83bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332  wex 1469   wcel 1481  wnfc 2269  wrex 2418 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423 This theorem is referenced by:  rexeq  2631
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