Theorem imp31 256

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

Hypothesis

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

Assertion

Ref	Expression
imp31	|- ( ( ( ph /\ ps ) /\ ch ) -> th )

Proof of Theorem imp31

Step	Hyp	Ref	Expression
1		imp3.1	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
2	1	imp 124	. 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:  imp41  353  imp5d  359  impl  380  anassrs  400  an31s  570  con4biddc  857  3imp  1193  3expa  1203  bilukdc  1396  reusv3  4458  dfimafn  5561  funimass4  5563  funimass3  5629  isopolem  5818  smores2  6290  tfrlem9  6315  nnmordi  6512  mulcanpig  7329  elnnz  9257  nzadd  9299  irradd  9640  irrmul  9641  uzsubsubfz  10040  fzo1fzo0n0  10176  elfzonelfzo  10223  infpnlem1  12347  tgcl  13346