Theorem anandi3r

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

	Ref	Expression
Assertion	anandi3r	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		3anan32	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )
2		anandir	|- ( ( ( ph /\ ch ) /\ ps ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )
3	1 2	bitri	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )