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Theorem euanv 2217
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 1609 . 2  |-  F/ x ph
21euan 2213 1  |-  ( E! x ( ph  /\  ps )  <->  ( ph  /\  E! x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E!weu 2156
This theorem is referenced by:  eueq2  2952  2reu5lem1  2983  fsn  5712  dfac5lem5  7770
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161
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