MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exp5l Structured version   Visualization version   Unicode version
Theorem exp5l 646
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5l.1 |- ( ph -> ( ( ( ps /\ ch ) /\ ( th /\ ta ) ) -> et ) )
Assertion
Ref Expression
exp5l |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Proof of Theorem exp5l
StepHypRef Expression
1 exp5l.1 . . 3 |- ( ph -> ( ( ( ps /\ ch ) /\ ( th /\ ta ) ) -> et ) )
21expd 452 . 2 |- ( ph -> ( ( ps /\ ch ) -> ( ( th /\ ta ) -> et ) ) )
32exp5c 644 1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Colors of variables: wff setvar class
Syntax hints:   -> wi 4   /\ wa 384
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 197  df-an 386
This theorem is referenced by:  erclwwlkstr  26936  erclwwlksntr  26948  exp512  32303
  Copyright terms: Public domain W3C validator