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Theorem pm4.52im 837
Description: One direction of theorem *4.52 of [WhiteheadRussell] p. 120. The converse also holds in classical logic. (Contributed by Jim Kingdon, 27-Jul-2018.)
Assertion
Ref Expression
pm4.52im  |-  ( (
ph  /\  -.  ps )  ->  -.  ( -.  ph  \/  ps ) )

Proof of Theorem pm4.52im
StepHypRef Expression
1 annimim 816 . 2  |-  ( (
ph  /\  -.  ps )  ->  -.  ( ph  ->  ps ) )
2 imorr 831 . 2  |-  ( ( -.  ph  \/  ps )  ->  ( ph  ->  ps ) )
31, 2nsyl 591 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:  pm4.53r  838
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