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Theorem rexex 2856
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 2755 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
2 exsimpr 1741 . 2  |-  ( E. x ( x  e.  A  /\  ph )  ->  E. x ph )
31, 2sylbi 200 1  |-  ( E. x  e.  A  ph  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 375   E.wex 1674    e. wcel 1898   E.wrex 2750
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675  df-rex 2755
This theorem is referenced by:  reu3  3240  rmo2i  3369  dffo5  6062  nqerf  9381  supsrlem  9561  vdwmc2  14978  isch3  26943  19.9d2rf  28161  volfiniune  29102  bnj594  29772  bnj1371  29887  bnj1374  29889  dfrdg4  30767  bj-0nelsngl  31610  bj-ccinftydisj  31700  poimirlem25  32010  mblfinlem3  32024  mblfinlem4  32025  stoweidlem57  37956
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