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Theorem rexeqi 2510
 Description: Equality inference for restricted existential qualifier. (Contributed by Mario Carneiro, 23-Apr-2015.)
Hypothesis
Ref Expression
raleq1i.1
Assertion
Ref Expression
rexeqi
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rexeqi
StepHypRef Expression
1 raleq1i.1 . 2
2 rexeq 2506 . 2
31, 2ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wb 98   wceq 1243  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312 This theorem is referenced by:  rexrab2  2708  rexprg  3422  rextpg  3424  rexxp  4480  rexrnmpt2  5616  arch  8178
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