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Theorem 19.23 1809
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 1808 . 2  |-  ( F/ x ps  ->  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) ) )
31, 2ax-mp 8 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530   E.wex 1531   F/wnf 1534
This theorem is referenced by:  nf2  1810  exlimi  1813  exlimd  1815  19.23v  1844  pm11.53  1846  ax10-16  2142  r19.3rz  3558  ralidm  3570  pm11.53g  25067  ax10ext  27709  pm11.53OLD7  29654
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-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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