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  3416  reupick  3420  po2nr  4310  fvmptt  5608  fliftfund  5798  f1ocnv2d  6075  addclpi  7326  addnidpig  7335  mulnqprl  7567  mulnqpru  7568  ltsubrp  9690  ltaddrp  9691  divgcdcoprm0  12101  infpnlem1  12357  innei  13666  tgcnp  13712  isxmetd  13850