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Theorem rexex 2362
Description: Restricted existence implies existence. (Contributed by NM, 11-Nov-1995.)
Assertion
Ref Expression
rexex (x A φxφ)

Proof of Theorem rexex
StepHypRef Expression
1 df-rex 2306 . 2 (x A φx(x A φ))
2 simpr 103 . . 3 ((x A φ) → φ)
32eximi 1488 . 2 (x(x A φ) → xφ)
41, 3sylbi 114 1 (x A φxφ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wex 1378   wcel 1390  wrex 2301
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-rex 2306
This theorem is referenced by:  reu3  2725  rmo2i  2842  dffo5  5259  halfnq  6394  nsmallnq  6396  0npr  6466  genpml  6500  genpmu  6501  ltexprlemm  6574  ltexprlemloc  6581
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