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Theorem 19.23 1656
Description: Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.23.1  |-  F/ x ps
Assertion
Ref Expression
19.23  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )

Proof of Theorem 19.23
StepHypRef Expression
1 19.23.1 . 2  |-  F/ x ps
2 19.23t 1655 . 2  |-  ( F/ x ps  ->  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) ) )
31, 2ax-mp 5 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1329   F/wnf 1436   E.wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  equsal  1705  r19.3rm  3451  ralidm  3463
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