Theorem 3impdi 1271

Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)

Hypothesis

Ref	Expression
3impdi.1	|- ( ( ( ph /\ ps ) /\ ( ph /\ ch ) ) -> th )

Assertion

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

Proof of Theorem 3impdi

Step	Hyp	Ref	Expression
1		3impdi.1	. . 3 |- ( ( ( ph /\ ps ) /\ ( ph /\ ch ) ) -> th )
2	1	anandis 581	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3impb 1177	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by:  ecovdi  6533  ecovidi  6534  distrpig  7134  mulcanenq  7186  mulcanenq0ec  7246  distrnq0  7260  axltadd  7827  absmulgcd  11694