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Theorem 19.37aiv 1912
Description: Inference from Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37aiv.1  |-  E. x
( ph  ->  ps )
Assertion
Ref Expression
19.37aiv  |-  ( ph  ->  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem 19.37aiv
StepHypRef Expression
1 19.37aiv.1 . 2  |-  E. x
( ph  ->  ps )
2 19.37v 1911 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
31, 2mpbi 200 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1547
This theorem is referenced by:  eqvinc  3006  bnd  7749  zfcndinf  8426  relopabVD  28354  bnj1093  28687  bnj1186  28714
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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