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Theorem 19.21 1795
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 1794 . 2  |-  ( F/ x ph  ->  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) ) )
31, 2ax-mp 10 1  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   F/wnf 1536
This theorem is referenced by:  19.21-2  1796  nf3  1803  19.32  1815  nfim1  1825  19.21v  1842  19.12vv  1850  ax15  2077  eu2  2169  moanim  2200  r2alf  2579  19.12b  23559  pm11.53g  24362  a12study2  28401
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-6 1707  ax-11 1719
This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1537
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