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Theorem jaoi3 970
Description: Inference separating a disjunct of an antecedent. (Contributed by Alexander van der Vekens, 25-May-2018.)
Hypotheses
Ref Expression
jaoi3.1  |-  ( ph  ->  ps )
jaoi3.2  |-  ( ( -.  ph  /\  ch )  ->  ps )
Assertion
Ref Expression
jaoi3  |-  ( (
ph  \/  ch )  ->  ps )

Proof of Theorem jaoi3
StepHypRef Expression
1 jaoi3.1 . . 3  |-  ( ph  ->  ps )
2 jaoi3.2 . . 3  |-  ( ( -.  ph  /\  ch )  ->  ps )
31, 2jaoi 377 . 2  |-  ( (
ph  \/  ( -.  ph 
/\  ch ) )  ->  ps )
43jaoi2 969 1  |-  ( (
ph  \/  ch )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 366    /\ wa 367
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 185  df-or 368  df-an 369
This theorem is referenced by:  bropopvvv  6863  ssnn0fi  12133  swrdnd  12711  2wlkonot3v  25279  2spthonot3v  25280
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