MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imp5g Unicode version
Theorem imp5g 584
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 419 . 2 |- ( ( ph /\ ps ) -> ( ch -> ( th -> ( ta -> et ) ) ) )
32imp4c 575 1 |- ( ( ph /\ ps ) -> ( ( ( ch /\ th ) /\ ta ) -> et ) )
Colors of variables: wff set class
Syntax hints:   -> wi 4   /\ wa 359
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361
  Copyright terms: Public domain W3C validator