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Theorem 19.37iv 1827
Description: Inference associated with 19.37v 1826. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37iv.1  |-  E. x
( ph  ->  ps )
Assertion
Ref Expression
19.37iv  |-  ( ph  ->  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem 19.37iv
StepHypRef Expression
1 19.37iv.1 . 2  |-  E. x
( ph  ->  ps )
2 19.37v 1826 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
31, 2mpbi 212 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805
This theorem depends on definitions:  df-bi 189  df-ex 1664
This theorem is referenced by:  eqvinc  3166  bnd  8363  zfcndinf  9043  bnj1093  29789  bnj1186  29816  relopabVD  37298
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