Theorem imp45 355

Description: An importation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
imp4.1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Assertion

Ref	Expression
imp45	|- ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) -> ta )

Proof of Theorem imp45

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	imp4d 350	. 2 |- ( ph -> ( ( ps /\ ( ch /\ th ) ) -> ta ) )
3	2	imp 123	1 |- ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)