Theorem imp5a

Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009) (Proof shortened by Wolf Lammen, 2-Aug-2022)

	Ref	Expression
Hypothesis	imp5.1	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Assertion	imp5a	|- ( ph -> ( ps -> ( ch -> ( ( th /\ ta ) -> et ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		imp5.1	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
2	1	imp5d	|- ( ( ( ph /\ ps ) /\ ch ) -> ( ( th /\ ta ) -> et ) )
3	2	exp31	|- ( ph -> ( ps -> ( ch -> ( ( th /\ ta ) -> et ) ) ) )