Theorem impancom 427

Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013.)

Hypothesis

Ref	Expression
impancom.1	|- ((ph /\ ps) -> (ch -> th))

Assertion

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

Proof of Theorem impancom

Step	Hyp	Ref	Expression
1		impancom.1	. . . 4 |- ((ph /\ ps) -> (ch -> th))
2	1	ex 423	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com23 72	. 2 |- (ph -> (ch -> (ps -> th)))
4	3	imp 418	1 |- ((ph /\ ch) -> (ps -> th))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  spimt  1974  eqrdav  2352