Theorem exp53 647

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 450	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ( ta -> et ) )
3	2	exp43 640	1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Syntax hints:   -> wi 4   /\ wa 384

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

This theorem is referenced by:  omordi  7646  xpdom2  8055  elfzodifsumelfzo  12533  grplcan  17477  grpolcan  27384