Theorem 3anandis 1283

Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 18-Apr-2007.)

Hypothesis

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

Assertion

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

Proof of Theorem 3anandis

Step	Hyp	Ref	Expression
1		simpl 443	. 2 |- ((ph /\ (ps /\ ch /\ th)) -> ph)
2		simpr1 961	. 2 |- ((ph /\ (ps /\ ch /\ th)) -> ps)
3		simpr2 962	. 2 |- ((ph /\ (ps /\ ch /\ th)) -> ch)
4		simpr3 963	. 2 |- ((ph /\ (ps /\ ch /\ th)) -> th)
5		3anandis.1	. 2 |- (((ph /\ ps) /\ (ph /\ ch) /\ (ph /\ th)) -> ta)
6	1, 2, 1, 3, 1, 4, 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)