Theorem exp42 371

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

Hypothesis

Ref	Expression
exp42.1	|- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta )

Assertion

Ref	Expression
exp42	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem exp42

Step	Hyp	Ref	Expression
1		exp42.1	. . 3 |- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta )
2	1	exp31 364	. 2 |- ( ph -> ( ( ps /\ ch ) -> ( th -> ta ) ) )
3	2	expd 258	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

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-ia3 108

This theorem is used by:  f1ocnv2d  6294  f1o3d  6298  issubg4m  13996  lmodvsdir  14649  lmodvsass  14650