Theorem imp4d 575

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

Hypothesis

Ref	Expression
imp4.1	|- (ph -> (ps -> (ch -> (th -> ta))))

Assertion

Ref	Expression
imp4d	|- (ph -> ((ps /\ (ch /\ th)) -> ta))

Proof of Theorem imp4d

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- (ph -> (ps -> (ch -> (th -> ta))))
2	1	imp4a 572	. 2 |- (ph -> (ps -> ((ch /\ th) -> ta)))
3	2	imp3a 420	1 |- (ph -> ((ps /\ (ch /\ th)) -> ta))

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:  imp45  580