Theorem 3impdir 881

Description: Importation inference (undistribute conjunction).

Hypothesis

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

Assertion

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

Proof of Theorem 3impdir

Step	Hyp	Ref	Expression
1		3impdir.1	. . 3 |- (((ph /\ ps) /\ (ch /\ ps)) -> th)
2	1	anandirs 513	. 2 |- (((ph /\ ch) /\ ps) -> th)
3	2	3impa 828	1 |- ((ph /\ ch /\ ps) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 775

This theorem is referenced by:  his7t 8956  his2sub2t 8959  hoadddirt 9730  nndivsub 10421

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 777

Copyright terms: Public domain