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Theorem imp5p 32305
Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
3imp5.1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Assertion
Ref Expression
imp5p |- ( ph -> ( ps -> ( ( ch /\ th /\ ta ) -> et ) ) )
Proof of Theorem imp5p
StepHypRef Expression
1 3imp5.1 . . . 4 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
21com52l 102 . . 3 |- ( ch -> ( th -> ( ta -> ( ph -> ( ps -> et ) ) ) ) )
323imp 1256 . 2 |- ( ( ch /\ th /\ ta ) -> ( ph -> ( ps -> et ) ) )
43com3l 89 1 |- ( ph -> ( ps -> ( ( ch /\ th /\ ta ) -> et ) ) )
Colors of variables: wff setvar class
Syntax hints:   -> wi 4   /\ w3a 1037
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  df-3an 1039
This theorem is referenced by: (None)
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