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Theorem 19.31 1795
Description: Theorem 19.31 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.31.1  |-  F/ x ps
Assertion
Ref Expression
19.31  |-  ( A. x ( ph  \/  ps )  <->  ( A. x ph  \/  ps ) )

Proof of Theorem 19.31
StepHypRef Expression
1 19.31.1 . . 3  |-  F/ x ps
2119.32 1794 . 2  |-  ( A. x ( ps  \/  ph )  <->  ( ps  \/  A. x ph ) )
3 orcom 378 . . 3  |-  ( (
ph  \/  ps )  <->  ( ps  \/  ph )
)
43albii 1554 . 2  |-  ( A. x ( ph  \/  ps )  <->  A. x ( ps  \/  ph ) )
5 orcom 378 . 2  |-  ( ( A. x ph  \/  ps )  <->  ( ps  \/  A. x ph ) )
62, 4, 53bitr4i 270 1  |-  ( A. x ( ph  \/  ps )  <->  ( A. x ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359   A.wal 1532   F/wnf 1539
This theorem is referenced by:  2eu3  2200  19.31vv  26950
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-nf 1540
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