Theorem anandi3

Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018)

	Ref	Expression
Assertion	anandi3	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		3anass	|- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2		anandi	|- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )
3	1 2	bitri	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )