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Theorem pm3.1 704
Description: Theorem *3.1 of [WhiteheadRussell] p. 111. The converse holds for decidable propositions, as seen at anordc 898. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm3.1  |-  ( (
ph  /\  ps )  ->  -.  ( -.  ph  \/  -.  ps ) )

Proof of Theorem pm3.1
StepHypRef Expression
1 pm3.14 703 . 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:  inssun  3211
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