Theorem anandi

Description: Distribution of conjunction over conjunction. (Contributed by NM, 14-Aug-1995)

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

Proof

Step	Hyp	Ref	Expression
1		anidm	|- ( ( ph /\ ph ) <-> ph )
2	1	anbi1i	|- ( ( ( ph /\ ph ) /\ ( ps /\ ch ) ) <-> ( ph /\ ( ps /\ ch ) ) )
3		an4	|- ( ( ( ph /\ ph ) /\ ( ps /\ ch ) ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )
4	2 3	bitr3i	|- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )