Theorem chjcli

Description: Closure of CH join. (Contributed by NM, 29-Jul-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ch0le.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
	chjcl.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	chjcli	$$⊢A{\vee }_{\mathscr{H}}B\in {\mathbf{C}}_{\mathscr{H}}$$

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		chjcl.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
3	1	chshii	$$⊢A\in {\mathbf{S}}_{\mathscr{H}}$$
4	2	chshii	$$⊢B\in {\mathbf{S}}_{\mathscr{H}}$$
5	3 4	shjcli	$$⊢A{\vee }_{\mathscr{H}}B\in {\mathbf{C}}_{\mathscr{H}}$$