Theorem 3anandirs 1284

Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.)

Hypothesis

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

Assertion

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

Proof of Theorem 3anandirs

Step	Hyp	Ref	Expression
1		simpl1 958	. 2 |- (((ph /\ ps /\ ch) /\ th) -> ph)
2		simpr 447	. 2 |- (((ph /\ ps /\ ch) /\ th) -> th)
3		simpl2 959	. 2 |- (((ph /\ ps /\ ch) /\ th) -> ps)
4		simpl3 960	. 2 |- (((ph /\ ps /\ ch) /\ th) -> ch)
5		3anandirs.1	. 2 |- (((ph /\ th) /\ (ps /\ th) /\ (ch /\ th)) -> ta)
6	1, 2, 3, 2, 4, 2, 5	syl222anc 1198	1 |- (((ph /\ ps /\ ch) /\ th) -> ta)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by: (None)