Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  jaoded Unicode version

Theorem jaoded 27705
Description: Deduction form of jao 498. Disjunction of antecedents. (Contributed by Alan Sare, 3-Dec-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
jaoded.1  |-  ( ph  ->  ( ps  ->  ch ) )
jaoded.2  |-  ( th 
->  ( ta  ->  ch ) )
jaoded.3  |-  ( et 
->  ( ps  \/  ta ) )
Assertion
Ref Expression
jaoded  |-  ( (
ph  /\  th  /\  et )  ->  ch )

Proof of Theorem jaoded
StepHypRef Expression
1 jaoded.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 jaoded.2 . 2  |-  ( th 
->  ( ta  ->  ch ) )
3 jaoded.3 . 2  |-  ( et 
->  ( ps  \/  ta ) )
4 jao 498 . . 3  |-  ( ( ps  ->  ch )  ->  ( ( ta  ->  ch )  ->  ( ( ps  \/  ta )  ->  ch ) ) )
543imp 1145 . 2  |-  ( ( ( ps  ->  ch )  /\  ( ta  ->  ch )  /\  ( ps  \/  ta ) )  ->  ch )
61, 2, 3, 5syl3an 1224 1  |-  ( (
ph  /\  th  /\  et )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ w3a 934
This theorem is referenced by:  suctrALT3  28073
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-3an 936
  Copyright terms: Public domain W3C validator