Theorem anandirs 804

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

Hypothesis

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

Assertion

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

Proof of Theorem anandirs

Step	Hyp	Ref	Expression
1		anandirs.1	. . 3 |- (((ph /\ ch) /\ (ps /\ ch)) -> ta)
2	1	an4s 799	. 2 |- (((ph /\ ps) /\ (ch /\ ch)) -> ta)
3	2	anabsan2 795	1 |- (((ph /\ ps) /\ ch) -> ta)

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  3impdir  1238  fvreseq  5399