Theorem exp41 370

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

Hypothesis

Ref	Expression
exp41.1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
exp41	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem exp41

Step	Hyp	Ref	Expression
1		exp41.1	. . 3 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
2	1	ex 115	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> ( th -> ta ) )
3	2	exp31 364	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:  apexp1  11156  swrdswrdlem  11476  swrdswrd  11477  nnnninfex  17065