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Theorem rexex 2422
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 2365 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
2 simpr 108 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ph )
32eximi 1536 . 2  |-  ( E. x ( x  e.  A  /\  ph )  ->  E. x ph )
41, 3sylbi 119 1  |-  ( E. x  e.  A  ph  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   E.wex 1426    e. wcel 1438   E.wrex 2360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-rex 2365
This theorem is referenced by:  reu3  2805  rmo2i  2929  dffo5  5442  halfnq  6960  nsmallnq  6962  0npr  7032  genpml  7066  genpmu  7067  ltexprlemm  7149  ltexprlemloc  7156
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