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Theorem imp55 627
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Assertion
Ref Expression
imp55 |- ( ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) /\ ta ) -> et )
Proof of Theorem imp55
StepHypRef Expression
1 imp5.1 . . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
21imp4a 614 . 2 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ( ta -> et ) ) ) )
32imp42 620 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:  alexsubALTlem4  21854
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