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Theorem 19.32 1812
Description: Theorem 19.32 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.32.1  |-  F/ x ph
Assertion
Ref Expression
19.32  |-  ( A. x ( ph  \/  ps )  <->  ( ph  \/  A. x ps ) )

Proof of Theorem 19.32
StepHypRef Expression
1 19.32.1 . . . 4  |-  F/ x ph
21nfn 1766 . . 3  |-  F/ x  -.  ph
3219.21 1792 . 2  |-  ( A. x ( -.  ph  ->  ps )  <->  ( -.  ph 
->  A. x ps )
)
4 df-or 361 . . 3  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
54albii 1554 . 2  |-  ( A. x ( ph  \/  ps )  <->  A. x ( -. 
ph  ->  ps ) )
6 df-or 361 . 2  |-  ( (
ph  \/  A. x ps )  <->  ( -.  ph  ->  A. x ps )
)
73, 5, 63bitr4i 270 1  |-  ( A. x ( ph  \/  ps )  <->  ( ph  \/  A. x ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178    \/ wo 359   A.wal 1528   F/wnf 1532
This theorem is referenced by:  19.31  1813  2eu3  2226  pm10.12  26952
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-nf 1533
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