Theorem exp5o 1170

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

Hypothesis

Ref	Expression
exp5o.1	|- ((ph /\ ps /\ ch) -> ((th /\ ta) -> et))

Assertion

Ref	Expression
exp5o	|- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Proof of Theorem exp5o

Step	Hyp	Ref	Expression
1		exp5o.1	. . 3 |- ((ph /\ ps /\ ch) -> ((th /\ ta) -> et))
2	1	exp3a 425	. 2 |- ((ph /\ ps /\ ch) -> (th -> (ta -> et)))
3	2	3exp 1150	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:  exp520  1172