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Theorem 19.37aiv 2034
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 2033 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
31, 2mpbi 201 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 6   E.wex 1537
This theorem is referenced by:  eqvinc  2846  bnd  7495  zfcndinf  8173  relopabVD  27690  bnj1093  28022  bnj1186  28049
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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