Theorem exp5o 1286

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 452	. 2 |- ( ( ph /\ ps /\ ch ) -> ( th -> ( ta -> et ) ) )
3	2	3exp 1264	1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

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  df-3an 1039

This theorem is referenced by:  exp520  1288  bndndx  11291  elicc3  32311  bgoldbtbndlem3  41695