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  4462  dfimafn  5566  funimass4  5568  funimass3  5634  isopolem  5825  smores2  6297  tfrlem9  6322  nnmordi  6519  mulcanpig  7336  elnnz  9265  nzadd  9307  irradd  9648  irrmul  9649  uzsubsubfz  10049  fzo1fzo0n0  10185  elfzonelfzo  10232  infpnlem1  12359  tgcl  13603