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Theorem 19.21h 1816
Description: Theorem 19.21 of [Margaris] p. 90. The hypothesis can be thought of as " x is not free in  ph." (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
Hypothesis
Ref Expression
19.21h.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
19.21h  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )

Proof of Theorem 19.21h
StepHypRef Expression
1 19.21h.1 . . 3  |-  ( ph  ->  A. x ph )
21nfi 1561 . 2  |-  F/ x ph
3219.21 1815 1  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   A.wal 1550
This theorem is referenced by:  hbim1  1830  ax12olem6OLD  2017  ax12olem6NEW7  29460
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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