Theorem exp53 600

Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009.)

Hypothesis

Ref	Expression
exp53.1	|- ((((ph /\ ps) /\ (ch /\ th)) /\ ta) -> et)

Assertion

Ref	Expression
exp53	|- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Proof of Theorem exp53

Step	Hyp	Ref	Expression
1		exp53.1	. . 3 |- ((((ph /\ ps) /\ (ch /\ th)) /\ ta) -> et)
2	1	ex 423	. 2 |- (((ph /\ ps) /\ (ch /\ th)) -> (ta -> et))
3	2	exp43 595	1 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Syntax hints:   -> wi 4   /\ wa 358

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

This theorem is referenced by: (None)