Theorem exp516 1171

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

Hypothesis

Ref	Expression
exp516.1	|- (((ph /\ (ps /\ ch /\ th)) /\ ta) -> et)

Assertion

Ref	Expression
exp516	|- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Proof of Theorem exp516

Step	Hyp	Ref	Expression
1		exp516.1	. . 3 |- (((ph /\ (ps /\ ch /\ th)) /\ ta) -> et)
2	1	exp31 587	. 2 |- (ph -> ((ps /\ ch /\ th) -> (ta -> et)))
3	2	3expd 1168	1 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Syntax hints:   -> wi 4   /\ wa 358   /\ 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: (None)