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Theorem pm4.53r 838
Description: One direction of theorem *4.53 of [WhiteheadRussell] p. 120. The converse also holds in classical logic. (Contributed by Jim Kingdon, 27-Jul-2018.)
Assertion
Ref Expression
pm4.53r  |-  ( ( -.  ph  \/  ps )  ->  -.  ( ph  /\ 
-.  ps ) )

Proof of Theorem pm4.53r
StepHypRef Expression
1 pm4.52im 837 . 2  |-  ( (
ph  /\  -.  ps )  ->  -.  ( -.  ph  \/  ps ) )
21con2i 590 1  |-  ( ( -.  ph  \/  ps )  ->  -.  ( ph  /\ 
-.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    \/ wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  undif3ss  3232
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