Theorem 3impexp 1366

Description: impexp 433 with a 3-conjunct antecedent. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

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

Proof of Theorem 3impexp

Step	Hyp	Ref	Expression
1		id 19	. . 3 |- (((ph /\ ps /\ ch) -> th) -> ((ph /\ ps /\ ch) -> th))
2	1	3expd 1168	. 2 |- (((ph /\ ps /\ ch) -> th) -> (ph -> (ps -> (ch -> th))))
3		id 19	. . 3 |- ((ph -> (ps -> (ch -> th))) -> (ph -> (ps -> (ch -> th))))
4	3	3impd 1165	. 2 |- ((ph -> (ps -> (ch -> th))) -> ((ph /\ ps /\ ch) -> th))
5	2, 4	impbii 180	1 |- (((ph /\ ps /\ ch) -> th) <-> (ph -> (ps -> (ch -> th))))

Syntax hints:   -> wi 4   <-> wb 176   /\ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by:  3impexpbicom  1367