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Theorem jaoian 742
Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005.)
Hypotheses
Ref Expression
jaoian.1  |-  ( (
ph  /\  ps )  ->  ch )
jaoian.2  |-  ( ( th  /\  ps )  ->  ch )
Assertion
Ref Expression
jaoian  |-  ( ( ( ph  \/  th )  /\  ps )  ->  ch )

Proof of Theorem jaoian
StepHypRef Expression
1 jaoian.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 113 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 113 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
52, 4jaoi 669 . 2  |-  ( (
ph  \/  th )  ->  ( ps  ->  ch ) )
65imp 122 1  |-  ( ( ( ph  \/  th )  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> 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-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ordi  763  ccase  906  faclbnd  9817  faclbnd3  9819
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