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 is referenced by:  imp5gOLD  26205

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

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