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Theorem 19.31 1812
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 1811 . 2  |-  ( A. x ( ps  \/  ph )  <->  ( ps  \/  A. x ph ) )
3 orcom 376 . . 3  |-  ( (
ph  \/  ps )  <->  ( ps  \/  ph )
)
43albii 1553 . 2  |-  ( A. x ( ph  \/  ps )  <->  A. x ( ps  \/  ph ) )
5 orcom 376 . 2  |-  ( ( A. x ph  \/  ps )  <->  ( ps  \/  A. x ph ) )
62, 4, 53bitr4i 268 1  |-  ( A. x ( ph  \/  ps )  <->  ( A. x ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357   A.wal 1527   F/wnf 1531
This theorem is referenced by:  2eu3  2225  19.31vv  27582
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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