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Theorem euanv 2032
Description: Introduction of a conjunct into unique existential 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 ax-17 1489 . 2  |-  ( ph  ->  A. x ph )
21euan 2031 1  |-  ( E! x ( ph  /\  ps )  <->  ( ph  /\  E! x ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   E!weu 1975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979
This theorem is referenced by:  eueq2dc  2828  fsn  5558
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