Theorem exp45 372

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

Hypothesis

Ref	Expression
exp45.1	|- ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) -> ta )

Assertion

Ref	Expression
exp45	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem exp45

Step	Hyp	Ref	Expression
1		exp45.1	. . 3 |- ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) -> ta )
2	1	exp32 363	. 2 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )
3	2	exp4a 364	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)