Theorem exp511 32302

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

Hypothesis

Ref	Expression
exp511.1	|- ( ( ph /\ ( ( ps /\ ( ch /\ th ) ) /\ ta ) ) -> et )

Assertion

Ref	Expression
exp511	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Proof of Theorem exp511

Step	Hyp	Ref	Expression
1		exp511.1	. . 3 |- ( ( ph /\ ( ( ps /\ ( ch /\ th ) ) /\ ta ) ) -> et )
2	1	ex 450	. 2 |- ( ph -> ( ( ( ps /\ ( ch /\ th ) ) /\ ta ) -> et ) )
3	2	exp5k 32298	1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by: (None)