Theorem imp55 343

Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)

Hypothesis

Ref	Expression
imp5.1	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Assertion

Ref	Expression
imp55	|- ( ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) /\ ta ) -> et )

Proof of Theorem imp55

Step	Hyp	Ref	Expression
1		imp5.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
2	1	imp4a 331	. 2 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ( ta -> et ) ) ) )
3	2	imp42 336	1 |- ( ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) /\ ta ) -> et )

Syntax hints:   -> wi 4   /\ wa 97

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

This theorem is referenced by: (None)