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Theorem 19.21 1803
Description: Theorem 19.21 of [Margaris] p. 90. The hypothesis can be thought of as " x is not free in  ph." (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.21.1  |-  F/ x ph
Assertion
Ref Expression
19.21  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )

Proof of Theorem 19.21
StepHypRef Expression
1 19.21.1 . 2  |-  F/ x ph
2 19.21t 1802 . 2  |-  ( F/ x ph  ->  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) ) )
31, 2ax-mp 8 1  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530   F/wnf 1534
This theorem is referenced by:  19.21-2  1804  nf3  1811  19.32  1823  nfim1  1833  19.21v  1843  19.12vv  1851  ax15  1974  eu2  2181  moanim  2212  r2alf  2591  19.12b  24229  pm11.53g  25067  ax15NEW7  29511  19.12vvOLD7  29655  a12study2  29756
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-nf 1535
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