Theorem 3impexp

Description: Version of impexp for a triple conjunction. (Contributed by Alan Sare, 31-Dec-2011)

	Ref	Expression
Assertion	3impexp	|- ( ( ( ph /\ ps /\ ch ) -> th ) <-> ( ph -> ( ps -> ( ch -> th ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ( ( ph /\ ps /\ ch ) -> th ) -> ( ( ph /\ ps /\ ch ) -> th ) )
2	1	3expd	|- ( ( ( ph /\ ps /\ ch ) -> th ) -> ( ph -> ( ps -> ( ch -> th ) ) ) )
3		id	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ph -> ( ps -> ( ch -> th ) ) ) )
4	3	3impd	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ( ph /\ ps /\ ch ) -> th ) )
5	2 4	impbii	|- ( ( ( ph /\ ps /\ ch ) -> th ) <-> ( ph -> ( ps -> ( ch -> th ) ) ) )