Theorem cmj1i

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

	Ref	Expression
Hypotheses	pjoml2.1	|- A e. CH
	pjoml2.2	|- B e. CH
Assertion	cmj1i	|- A C_H ( A vH B )

Proof

Step	Hyp	Ref	Expression
1		pjoml2.1	|- A e. CH
2		pjoml2.2	|- B e. CH
3	1 2	chjcli	|- ( A vH B ) e. CH
4	1 2	chub1i	|- A C_ ( A vH B )
5	1 3 4	lecmii	|- A C_H ( A vH B )