Theorem exp516 1222

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Hypothesis

Ref	Expression
exp516.1	|- ( ( ( ph /\ ( ps /\ ch /\ th ) ) /\ ta ) -> et )

Assertion

Ref	Expression
exp516	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Proof of Theorem exp516

Step	Hyp	Ref	Expression
1		exp516.1	. . 3 |- ( ( ( ph /\ ( ps /\ ch /\ th ) ) /\ ta ) -> et )
2	1	exp31 362	. 2 |- ( ph -> ( ( ps /\ ch /\ th ) -> ( ta -> et ) ) )
3	2	3expd 1219	1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

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  df-3an 975

This theorem is referenced by: (None)