Theorem 3impd 1118

Description: Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

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

Assertion

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

Proof of Theorem 3impd

Step	Hyp	Ref	Expression
1		3imp1.1	. . . 4 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	com4l 78	. . 3 |- ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )
3	2	3imp 1098	. 2 |- ( ( ps /\ ch /\ th ) -> ( ph -> ta ) )
4	3	com12 27	1 |- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )

Syntax hints:   -> wi 4   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  3imp2  1119  3impexp  1326  oprabid  5537  iccid  8794