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  1204  reuss2  3415  reupick  3419  po2nr  4309  fvmptt  5607  fliftfund  5797  f1ocnv2d  6074  addclpi  7325  addnidpig  7334  mulnqprl  7566  mulnqpru  7567  ltsubrp  9688  ltaddrp  9689  divgcdcoprm0  12095  infpnlem1  12351  innei  13594  tgcnp  13640  isxmetd  13778