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Theorem imorr 695
Description: Implication in terms of disjunction. One direction of theorem *4.6 of [WhiteheadRussell] p. 120. The converse holds for decidable propositions, as seen at imordc 867. (Contributed by Jim Kingdon, 21-Jul-2018.)
Assertion
Ref Expression
imorr  |-  ( ( -.  ph  \/  ps )  ->  ( ph  ->  ps ) )

Proof of Theorem imorr
StepHypRef Expression
1 ax-in2 589 . 2  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
2 ax-1 6 . 2  |-  ( ps 
->  ( ph  ->  ps ) )
31, 2jaoi 690 1  |-  ( ( -.  ph  \/  ps )  ->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm4.52im  724  nf4r  1634
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