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Theorem 19.32 1811
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 1765 . . 3  |-  F/ x  -.  ph
3219.21 1791 . 2  |-  ( A. x ( -.  ph  ->  ps )  <->  ( -.  ph 
->  A. x ps )
)
4 df-or 359 . . 3  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
54albii 1553 . 2  |-  ( A. x ( ph  \/  ps )  <->  A. x ( -. 
ph  ->  ps ) )
6 df-or 359 . 2  |-  ( (
ph  \/  A. x ps )  <->  ( -.  ph  ->  A. x ps )
)
73, 5, 63bitr4i 268 1  |-  ( A. x ( ph  \/  ps )  <->  ( ph  \/  A. x ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357   A.wal 1527   F/wnf 1531
This theorem is referenced by:  19.31  1812  2eu3  2225  pm10.12  26965
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-nf 1532
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