Theorem 3imp1 1215

Description: Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Hypothesis

Ref	Expression
3imp1.1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Assertion

Ref	Expression
3imp1	|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Proof of Theorem 3imp1

Step	Hyp	Ref	Expression
1		3imp1.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	3imp 1188	. 2 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
3	2	imp 123	1 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

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

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  reupick2  3413  ledivge1le  9683  leexp1a  10531