Theorem imp5g 583

Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)

Hypothesis

Ref	Expression
imp5.1	|- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Assertion

Ref	Expression
imp5g	|- ((ph /\ ps) -> (((ch /\ th) /\ ta) -> et))

Proof of Theorem imp5g

Step	Hyp	Ref	Expression
1		imp5.1	. . 3 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))
2	1	imp 418	. 2 |- ((ph /\ ps) -> (ch -> (th -> (ta -> et))))
3	2	imp4c 574	1 |- ((ph /\ ps) -> (((ch /\ th) /\ ta) -> et))

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: (None)