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  569  3expb  1231  reuss2  3489  reupick  3493  po2nr  4412  fvmptt  5747  fliftfund  5948  f1ocnv2d  6237  addclpi  7607  addnidpig  7616  mulnqprl  7848  mulnqpru  7849  ltsubrp  9986  ltaddrp  9987  pfxccat3  11381  divgcdcoprm0  12753  infpnlem1  13012  imasmnd2  13615  imasgrp2  13777  imasrng  14050  imasring  14158  innei  14974  tgcnp  15020  isxmetd  15158  2lgslem1a1  15905