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Theorem pm4.52 477
Description: Theorem *4.52 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)
Assertion
Ref Expression
pm4.52  |-  ( (
ph  /\  -.  ps )  <->  -.  ( -.  ph  \/  ps ) )

Proof of Theorem pm4.52
StepHypRef Expression
1 annim 414 . 2  |-  ( (
ph  /\  -.  ps )  <->  -.  ( ph  ->  ps ) )
2 imor 401 . 2  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
31, 2xchbinx 301 1  |-  ( (
ph  /\  -.  ps )  <->  -.  ( -.  ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  pm4.53  478
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
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