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Theorem 19.37aiv 1853
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 1852 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
31, 2mpbi 199 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1531
This theorem is referenced by:  eqvinc  2908  bnd  7578  zfcndinf  8256  relopabVD  28993  bnj1093  29326  bnj1186  29353
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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