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Theorem exp5k 32298
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5k.1 |- ( ph -> ( ( ( ps /\ ( ch /\ th ) ) /\ ta ) -> et ) )
Assertion
Ref Expression
exp5k |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Proof of Theorem exp5k
StepHypRef Expression
1 exp5k.1 . . 3 |- ( ph -> ( ( ( ps /\ ( ch /\ th ) ) /\ ta ) -> et ) )
21expd 452 . 2 |- ( ph -> ( ( ps /\ ( ch /\ th ) ) -> ( ta -> et ) ) )
32exp4d 637 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:  exp511  32302
  Copyright terms: Public domain W3C validator