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Theorem 19.21h 1912
Description: Theorem 19.21 of [Margaris] p. 90. The hypothesis can be thought of as " x is not free in  ph." See also 19.21 1910 and 19.21v 1734. (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 1628 . 2  |-  F/ x ph
3219.21 1910 1  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-ex 1618  df-nf 1622
This theorem is referenced by:  hbim1  1923
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