Theorem 3impdi 1293

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 592	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3impb 1199	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

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

This theorem is referenced by:  ecovdi  6642  ecovidi  6643  distrpig  7328  mulcanenq  7380  mulcanenq0ec  7440  distrnq0  7454  axltadd  8022  absmulgcd  12009