Theorem exp5o 1123

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 245	. 2 |- ( ( ph /\ ps /\ ch ) -> ( th -> ( ta -> et ) ) )
3	2	3exp 1103	1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  exp520  1125  bndndx  8180