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Theorem 3jaodd 24065
Description: Double deduction form of 3jaoi 1245. (Contributed by Scott Fenton, 20-Apr-2011.)
Hypotheses
Ref Expression
3jaodd.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
3jaodd.2  |-  ( ph  ->  ( ps  ->  ( th  ->  et ) ) )
3jaodd.3  |-  ( ph  ->  ( ps  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
3jaodd  |-  ( ph  ->  ( ps  ->  (
( ch  \/  th  \/  ta )  ->  et ) ) )

Proof of Theorem 3jaodd
StepHypRef Expression
1 3jaodd.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
21com3r 73 . . 3  |-  ( ch 
->  ( ph  ->  ( ps  ->  et ) ) )
3 3jaodd.2 . . . 4  |-  ( ph  ->  ( ps  ->  ( th  ->  et ) ) )
43com3r 73 . . 3  |-  ( th 
->  ( ph  ->  ( ps  ->  et ) ) )
5 3jaodd.3 . . . 4  |-  ( ph  ->  ( ps  ->  ( ta  ->  et ) ) )
65com3r 73 . . 3  |-  ( ta 
->  ( ph  ->  ( ps  ->  et ) ) )
72, 4, 63jaoi 1245 . 2  |-  ( ( ch  \/  th  \/  ta )  ->  ( ph  ->  ( ps  ->  et ) ) )
87com3l 75 1  |-  ( ph  ->  ( ps  ->  (
( ch  \/  th  \/  ta )  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ w3o 933
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  df-3or 935  df-3an 936
  Copyright terms: Public domain W3C validator