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Theorem rexex 2385
Description: Restricted existence implies existence. (Contributed by NM, 11-Nov-1995.)
Assertion
Ref Expression
rexex  |-  ( E. x  e.  A  ph  ->  E. x ph )

Proof of Theorem rexex
StepHypRef Expression
1 df-rex 2329 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
2 simpr 107 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ph )
32eximi 1507 . 2  |-  ( E. x ( x  e.  A  /\  ph )  ->  E. x ph )
41, 3sylbi 118 1  |-  ( E. x  e.  A  ph  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101   E.wex 1397    e. wcel 1409   E.wrex 2324
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-rex 2329
This theorem is referenced by:  reu3  2754  rmo2i  2876  dffo5  5344  halfnq  6567  nsmallnq  6569  0npr  6639  genpml  6673  genpmu  6674  ltexprlemm  6756  ltexprlemloc  6763
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