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Theorem jaao 497
Description: Inference conjoining and disjoining the antecedents of two implications. (Contributed by NM, 30-Sep-1999.)
Hypotheses
Ref Expression
jaao.1  |-  ( ph  ->  ( ps  ->  ch ) )
jaao.2  |-  ( th 
->  ( ta  ->  ch ) )
Assertion
Ref Expression
jaao  |-  ( (
ph  /\  th )  ->  ( ( ps  \/  ta )  ->  ch )
)

Proof of Theorem jaao
StepHypRef Expression
1 jaao.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21adantr 453 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 jaao.2 . . 3  |-  ( th 
->  ( ta  ->  ch ) )
43adantl 454 . 2  |-  ( (
ph  /\  th )  ->  ( ta  ->  ch ) )
52, 4jaod 371 1  |-  ( (
ph  /\  th )  ->  ( ( ps  \/  ta )  ->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 359    /\ wa 360
This theorem is referenced by:  pm3.44  499  pm3.48  808  prlem1  930  ordtri1  4643  ordun  4712  suc11  4714  funun  5524  poxp  6487  suc11reg  7603  rankunb  7805  gruun  8712  sibfof  24685
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 179  df-or 361  df-an 362
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