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Theorem pm4.54 495
Description: Theorem *4.54 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)
Assertion
Ref Expression
pm4.54  |-  ( ( -.  ph  /\  ps )  <->  -.  ( ph  \/  -.  ps ) )

Proof of Theorem pm4.54
StepHypRef Expression
1 df-an 372 . 2  |-  ( ( -.  ph  /\  ps )  <->  -.  ( -.  ph  ->  -. 
ps ) )
2 pm4.66 421 . 2  |-  ( ( -.  ph  ->  -.  ps ) 
<->  ( ph  \/  -.  ps ) )
31, 2xchbinx 311 1  |-  ( ( -.  ph  /\  ps )  <->  -.  ( ph  \/  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    \/ wo 369    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372
This theorem is referenced by:  pm4.55  496
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