Theorem anasss 628

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by NM, 15-Nov-2002.)

Hypothesis

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

Assertion

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

Proof of Theorem anasss

Step	Hyp	Ref	Expression
1		anasss.1	. . 3 |- (((ph /\ ps) /\ ch) -> th)
2	1	exp31 587	. 2 |- (ph -> (ps -> (ch -> th)))
3	2	imp32 422	1 |- ((ph /\ (ps /\ ch)) -> th)

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:  anass  630  anabss3  796  ncfinraise  4482  f1elima  5475