Theorem exp5c 374

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

Hypothesis

Ref	Expression
exp5c.1	|- ( ph -> ( ( ps /\ ch ) -> ( ( th /\ ta ) -> et ) ) )

Assertion

Ref	Expression
exp5c	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Proof of Theorem exp5c

Step	Hyp	Ref	Expression
1		exp5c.1	. . 3 |- ( ph -> ( ( ps /\ ch ) -> ( ( th /\ ta ) -> et ) ) )
2	1	exp4a 364	. 2 |- ( ph -> ( ( ps /\ ch ) -> ( th -> ( ta -> et ) ) ) )
3	2	expd 256	1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  fiintim  6894