Theorem shjshcli

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

	Ref	Expression
Hypotheses	shincl.1	⊢ 𝐴 ∈ Sℋ
	shincl.2	⊢ 𝐵 ∈ Sℋ
Assertion	shjshcli	⊢ ( 𝐴 ∨ℋ 𝐵 ) ∈ Sℋ

Proof

Step	Hyp	Ref	Expression
1		shincl.1	⊢ 𝐴 ∈ Sℋ
2		shincl.2	⊢ 𝐵 ∈ Sℋ
3	1 2	shjcli	⊢ ( 𝐴 ∨ℋ 𝐵 ) ∈ Cℋ
4	3	chshii	⊢ ( 𝐴 ∨ℋ 𝐵 ) ∈ Sℋ