Theorem imp55 361

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 349	. 2 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ( ta -> et ) ) ) )
3	2	imp42 354	1 |- ( ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) /\ ta ) -> et )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by: (None)