Theorem 3impd 1221

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 84	. . 3 |- ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )
3	2	3imp 1193	. 2 |- ( ( ps /\ ch /\ th ) -> ( ph -> ta ) )
4	3	com12 30	1 |- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )

Syntax hints:   -> wi 4   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem depends on definitions:  df-bi 117  df-3an 980

This theorem is referenced by:  3imp2  1222  3impexp  1437  oprabid  5909  iccid  9927  issubg4m  13058