Theorem chlej1i

Description: Add join to both sides of a Hilbert lattice ordering. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ch0le.1	|- A e. CH
	chjcl.2	|- B e. CH
	chlub.1	|- C e. CH
Assertion	chlej1i	|- ( A C_ B -> ( A vH C ) C_ ( B vH C ) )

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	|- A e. CH
2		chjcl.2	|- B e. CH
3		chlub.1	|- C e. CH
4	1	chshii	|- A e. SH
5	2	chshii	|- B e. SH
6	3	chshii	|- C e. SH
7	4 5 6	shlej1i	|- ( A C_ B -> ( A vH C ) C_ ( B vH C ) )