Theorem imp4c 574

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

Hypothesis

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

Assertion

Ref	Expression
imp4c	|- (ph -> (((ps /\ ch) /\ th) -> ta))

Proof of Theorem imp4c

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- (ph -> (ps -> (ch -> (th -> ta))))
2	1	imp3a 420	. 2 |- (ph -> ((ps /\ ch) -> (th -> ta)))
3	2	imp3a 420	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:  imp44  579  imp5g  583