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Theorem euanv 2005
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 1464 . 2  |-  ( ph  ->  A. x ph )
21euan 2004 1  |-  ( E! x ( ph  /\  ps )  <->  ( ph  /\  E! x ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103   E!weu 1948
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-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952
This theorem is referenced by:  eueq2dc  2788  fsn  5469
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