Theorem exp45 597

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp45.1	|- ((ph /\ (ps /\ (ch /\ th))) -> ta)

Assertion

Ref	Expression
exp45	|- (ph -> (ps -> (ch -> (th -> ta))))

Proof of Theorem exp45

Step	Hyp	Ref	Expression
1		exp45.1	. . 3 |- ((ph /\ (ps /\ (ch /\ th))) -> ta)
2	1	exp32 588	. 2 |- (ph -> (ps -> ((ch /\ th) -> ta)))
3	2	exp4a 589	1 |- (ph -> (ps -> (ch -> (th -> ta))))

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)