Theorem imp32 257

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	impd 254	. 2 |- ( ph -> ( ( ps /\ ch ) -> th ) )
3	2	imp 124	1 |- ( ( ph /\ ( ps /\ ch ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem is referenced by:  imp42  354  impr  379  anasss  399  an13s  567  3expb  1228  reuss2  3484  reupick  3488  po2nr  4400  fvmptt  5726  fliftfund  5921  f1ocnv2d  6210  addclpi  7514  addnidpig  7523  mulnqprl  7755  mulnqpru  7756  ltsubrp  9886  ltaddrp  9887  pfxccat3  11266  divgcdcoprm0  12623  infpnlem1  12882  imasmnd2  13485  imasgrp2  13647  imasrng  13919  imasring  14027  innei  14837  tgcnp  14883  isxmetd  15021  2lgslem1a1  15765