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Theorem euanv 2342
Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
euanv  |-  ( E! x ( ph  /\  ps )  <->  ( ph  /\  E! x ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem euanv
StepHypRef Expression
1 nfv 1629 . 2  |-  F/ x ph
21euan 2338 1  |-  ( E! x ( ph  /\  ps )  <->  ( ph  /\  E! x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359   E!weu 2281
This theorem is referenced by:  eueq2  3108  2reu5lem1  3139  fsn  5906  dfac5lem5  8008
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286
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