Theorem imp5q 32306

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
imp5q	|- ( ( ph /\ ps ) -> ( ( ch /\ th /\ ta ) -> et ) )

Proof of Theorem imp5q

Step	Hyp	Ref	Expression
1		3imp5.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
2	1	imp 445	. 2 |- ( ( ph /\ ps ) -> ( ch -> ( th -> ( ta -> et ) ) ) )
3	2	3impd 1281	1 |- ( ( ph /\ ps ) -> ( ( ch /\ th /\ ta ) -> et ) )

Syntax hints:   -> wi 4   /\ wa 384   /\ 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:  elicc3  32311