Theorem shjshcli

Description: SH closure of join. (Contributed by NM, 5-May-2000) (New usage is discouraged.)

	Ref	Expression
Hypotheses	shincl.1	$$⊢A\in {\mathbf{S}}_{\mathscr{H}}$$
	shincl.2	$$⊢B\in {\mathbf{S}}_{\mathscr{H}}$$
Assertion	shjshcli	$$⊢A{\vee }_{\mathscr{H}}B\in {\mathbf{S}}_{\mathscr{H}}$$

Proof

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