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Metamath Proof Explorer

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