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Theorem jaao 495
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 451 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 jaao.2 . . 3  |-  ( th 
->  ( ta  ->  ch ) )
43adantl 452 . 2  |-  ( (
ph  /\  th )  ->  ( ta  ->  ch ) )
52, 4jaod 369 1  |-  ( (
ph  /\  th )  ->  ( ( ps  \/  ta )  ->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ wa 358
This theorem is referenced by:  pm3.44  497  pm3.48  806  prlem1  928  ordtri1  4427  ordun  4496  suc11  4498  funun  5298  poxp  6229  suc11reg  7322  rankunb  7524  gruun  8430
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
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