Theorem imp32 422

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

Hypothesis

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

Assertion

Ref	Expression
imp32	|- ((ph /\ (ps /\ ch)) -> th)

Proof of Theorem imp32

Step	Hyp	Ref	Expression
1		imp3.1	. . 3 |- (ph -> (ps -> (ch -> th)))
2	1	imp3a 420	. 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:  imp42  577  impr  602  anasss  628  an13s  778  3expb  1152  reuss2  3536  reupick  3540  tfinnn  4535  f1o2d  5728