Theorem anandir

Description: Distribution of conjunction over conjunction. (Contributed by NM, 24-Aug-1995)

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

Proof

Step	Hyp	Ref	Expression
1		anidm	|- ( ( ch /\ ch ) <-> ch )
2	1	anbi2i	|- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) <-> ( ( ph /\ ps ) /\ ch ) )
3		an4	|- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ ch ) ) )
4	2 3	bitr3i	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ( ps /\ ch ) ) )