MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exp5c Structured version   Unicode version

Theorem exp5c 620
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5c.1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ( th  /\  ta )  ->  et ) ) )
Assertion
Ref Expression
exp5c  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp5c
StepHypRef Expression
1 exp5c.1 . . 3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ( th  /\  ta )  ->  et ) ) )
21exp4a 610 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( th 
->  ( ta  ->  et ) ) ) )
32expd 438 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 371
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 189  df-an 373
This theorem is referenced by:  fiint  7852  inf3lem2  8138  fgcl  20885  exp5l  30959  pclfinN  33390  hbtlem2  35909
  Copyright terms: Public domain W3C validator