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

Theorem exp5d 30361
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 ) )
21expd 434 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( th  ->  ( ta  ->  et ) ) )
32exp31 602 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367
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 185  df-an 369
This theorem is referenced by:  exp56  30366
  Copyright terms: Public domain W3C validator