Theorem exp53 377

Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009.)

Hypothesis

Ref	Expression
exp53.1	|- ( ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) /\ ta ) -> et )

Assertion

Ref	Expression
exp53	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Proof of Theorem exp53

Step	Hyp	Ref	Expression
1		exp53.1	. . 3 |- ( ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) /\ ta ) -> et )
2	1	ex 115	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ( ta -> et ) )
3	2	exp43 372	1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  xpdom2  6890  elfzodifsumelfzo  10277  grplcan  13194