Theorem anasss

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

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

Proof

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