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Theorem 19.23 1798
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 1797 . 2  |-  ( F/ x ps  ->  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) ) )
31, 2ax-mp 10 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1528   E.wex 1529   F/wnf 1532
This theorem is referenced by:  nf2  1799  exlimi  1802  exlimd  1804  19.23v  1833  pm11.53  1835  ax10-16  2131  r19.3rz  3546  ralidm  3558  pm11.53g  24362  ax10ext  27005
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1530  df-nf 1533
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