Theorem imp5p

Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009)

	Ref	Expression
Hypothesis	3imp5.1	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Assertion	imp5p	|- ( ph -> ( ps -> ( ( ch /\ th /\ ta ) -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		3imp5.1	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
2	1	com52l	|- ( ch -> ( th -> ( ta -> ( ph -> ( ps -> et ) ) ) ) )
3	2	3imp	|- ( ( ch /\ th /\ ta ) -> ( ph -> ( ps -> et ) ) )
4	3	com3l	|- ( ph -> ( ps -> ( ( ch /\ th /\ ta ) -> et ) ) )