Users' Mathboxes Mathbox for Jeff Hankins < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  exp5d Unicode version

Theorem exp5d 26311
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5d.1  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( ( th  /\  ta )  ->  et ) )
Assertion
Ref Expression
exp5d  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp5d
StepHypRef Expression
1 exp5d.1 . . 3  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( ( th  /\  ta )  ->  et ) )
21exp3a 425 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( th  ->  ( ta  ->  et ) ) )
32exp31 587 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  exp56  26316
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-an 360
  Copyright terms: Public domain W3C validator