Theorem chub2i

Description: CH join is an upper bound of two elements. (Contributed by NM, 5-Nov-2000) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ch0le.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
	chjcl.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	chub2i	$$⊢A\subseteq B{\vee }_{\mathscr{H}}A$$

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 2	chub1i	$$⊢A\subseteq A{\vee }_{\mathscr{H}}B$$
4	1 2	chjcomi	$$⊢A{\vee }_{\mathscr{H}}B=B{\vee }_{\mathscr{H}}A$$
5	3 4	sseqtri	$$⊢A\subseteq B{\vee }_{\mathscr{H}}A$$