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Theorem 19.21 1516
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 1515 . 2  |-  ( F/ x ph  ->  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) ) )
31, 2ax-mp 7 1  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1283   F/wnf 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  stdpc5  1517  19.21-2  1598  19.32dc  1610  cbv1  1674  eu2  1987  mo3h  1996  moanim  2017  r2alf  2388
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