Theorem imp31 421

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

Hypothesis

Ref	Expression
imp3.1	|- (ph -> (ps -> (ch -> th)))

Assertion

Ref	Expression
imp31	|- (((ph /\ ps) /\ ch) -> th)

Proof of Theorem imp31

Step	Hyp	Ref	Expression
1		imp3.1	. . 3 |- (ph -> (ps -> (ch -> th)))
2	1	imp 418	. 2 |- ((ph /\ ps) -> (ch -> th))
3	2	imp 418	1 |- (((ph /\ ps) /\ ch) -> th)

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:  imp41  576  imp5d  582  impl  603  anassrs  629  an31s  781  3imp  1145  3expa  1151  ncfinraise  4481  evenodddisj  4516  funimass3  5404