Theorem cmm1i

Description: A Hilbert lattice element commutes with its meet. (Contributed by NM, 7-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	pjoml2.1	|- A e. CH
	pjoml2.2	|- B e. CH
Assertion	cmm1i	|- A C_H ( A i^i B )

Proof

Step	Hyp	Ref	Expression
1		pjoml2.1	|- A e. CH
2		pjoml2.2	|- B e. CH
3	1 2	chincli	|- ( A i^i B ) e. CH
4		inss1	|- ( A i^i B ) C_ A
5	3 1 4	lecmii	|- ( A i^i B ) C_H A
6	3 1 5	cmcmii	|- A C_H ( A i^i B )