Theorem anass

Description: Associative law for conjunction. Theorem *4.32 of WhiteheadRussell p. 118. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Assertion	anass	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ( ph /\ ( ps /\ ch ) ) -> ( ph /\ ( ps /\ ch ) ) )
2	1	anassrs	|- ( ( ( ph /\ ps ) /\ ch ) -> ( ph /\ ( ps /\ ch ) ) )
3		id	|- ( ( ( ph /\ ps ) /\ ch ) -> ( ( ph /\ ps ) /\ ch ) )
4	3	anasss	|- ( ( ph /\ ( ps /\ ch ) ) -> ( ( ph /\ ps ) /\ ch ) )
5	2 4	impbii	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )