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Theorem imp5g 585
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
imp5g |- ( ( ph /\ ps ) -> ( ( ( ch /\ th ) /\ ta ) -> et ) )
Proof of Theorem imp5g
StepHypRef Expression
1 imp5.1 . . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
21imp 420 . 2 |- ( ( ph /\ ps ) -> ( ch -> ( th -> ( ta -> et ) ) ) )
32imp4c 576 1 |- ( ( ph /\ ps ) -> ( ( ( ch /\ th ) /\ ta ) -> et ) )
Colors of variables: wff set class
Syntax hints:   -> wi 4   /\ wa 360
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 179  df-an 362
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