Theorem anandis 803

Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)

Hypothesis

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

Assertion

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

Proof of Theorem anandis

Step	Hyp	Ref	Expression
1		anandis.1	. . 3 |- (((ph /\ ps) /\ (ph /\ ch)) -> ta)
2	1	an4s 799	. 2 |- (((ph /\ ph) /\ (ps /\ ch)) -> ta)
3	2	anabsan 786	1 |- ((ph /\ (ps /\ ch)) -> ta)

Syntax hints:   -> wi 4   /\ wa 358

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

This theorem is referenced by:  3impdi  1237  dff13  5472  isotr  5496  f1oiso  5500