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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 ∈ S ℋ
shincl.2 ⊢ B ∈ S ℋ
Assertion shjshcli ⊢ A ∨ ℋ B ∈ S ℋ

Proof

Step Hyp Ref Expression
1 shincl.1 ⊢ A ∈ S ℋ
2 shincl.2 ⊢ B ∈ S ℋ
3 1 2 shjcli ⊢ A ∨ ℋ B ∈ C ℋ
4 3 chshii ⊢ A ∨ ℋ B ∈ S ℋ