Theorem imp41 351

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

Hypothesis

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

Assertion

Ref	Expression
imp41	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Proof of Theorem imp41

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	imp 123	. 2 |- ( ( ph /\ ps ) -> ( ch -> ( th -> ta ) ) )
3	2	imp31 254	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

This theorem is referenced by:  3anassrs  1224  lemul12a  8778  dvdsprmpweqle  12290  grpinveu  12741