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Theorem jaoi2 959
Description: Inference removing a negated conjunct in a disjunction of an antecedent if this conjunct is part of the disjunction. (Contributed by Alexander van der Vekens, 3-Nov-2017.) (Proof shortened by Wolf Lammen, 21-Sep-2018.)
Hypothesis
Ref Expression
jaoi2.1  |-  ( (
ph  \/  ( -.  ph 
/\  ch ) )  ->  ps )
Assertion
Ref Expression
jaoi2  |-  ( (
ph  \/  ch )  ->  ps )

Proof of Theorem jaoi2
StepHypRef Expression
1 pm5.63 915 . 2  |-  ( (
ph  \/  ch )  <->  (
ph  \/  ( -.  ph 
/\  ch ) ) )
2 jaoi2.1 . 2  |-  ( (
ph  \/  ( -.  ph 
/\  ch ) )  ->  ps )
31, 2sylbi 195 1  |-  ( (
ph  \/  ch )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368    /\ wa 369
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 370  df-an 371
This theorem is referenced by:  jaoi3  961  bropopvvv  6764  2wlkonot3v  30543  2spthonot3v  30544
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