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Theorem 19.31 2025
Description: Theorem 19.31 of [Margaris] p. 90. See 19.31v 1782 for a version requiring fewer axioms. (Contributed by NM, 14-May-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 2024 . 2  |-  ( A. x ( ps  \/  ph )  <->  ( ps  \/  A. x ph ) )
3 orcom 388 . . 3  |-  ( (
ph  \/  ps )  <->  ( ps  \/  ph )
)
43albii 1687 . 2  |-  ( A. x ( ph  \/  ps )  <->  A. x ( ps  \/  ph ) )
5 orcom 388 . 2  |-  ( ( A. x ph  \/  ps )  <->  ( ps  \/  A. x ph ) )
62, 4, 53bitr4i 280 1  |-  ( A. x ( ph  \/  ps )  <->  ( A. x ph  \/  ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    \/ wo 369   A.wal 1435   F/wnf 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907
This theorem depends on definitions:  df-bi 188  df-or 371  df-ex 1660  df-nf 1664
This theorem is referenced by:  2eu3  2357
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