MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exp53 Unicode version

Theorem exp53 600
Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009.)
Hypothesis
Ref Expression
exp53.1  |-  ( ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  /\  ta )  ->  et )
Assertion
Ref Expression
exp53  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp53
StepHypRef Expression
1 exp53.1 . . 3  |-  ( ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  /\  ta )  ->  et )
21ex 423 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  ->  ( ta  ->  et ) )
32exp43 595 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  omordi  6564  xpdom2  6957  grplcan  14534  grpolcan  20900
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