Theorem exp5o 1221

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

Hypothesis

Ref	Expression
exp5o.1	|- ( ( ph /\ ps /\ ch ) -> ( ( th /\ ta ) -> et ) )

Assertion

Ref	Expression
exp5o	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Proof of Theorem exp5o

Step	Hyp	Ref	Expression
1		exp5o.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> ( ( th /\ ta ) -> et ) )
2	1	expd 256	. 2 |- ( ( ph /\ ps /\ ch ) -> ( th -> ( ta -> et ) ) )
3	2	3exp 1197	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:  exp520  1223  bndndx  9134