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Metamath Proof Explorer

Theorem chjcli

Description: Closure of CH join. (Contributed by NM, 29-Jul-1999) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1 ⊢ A ∈ C ℋ
chjcl.2 ⊢ B ∈ C ℋ
Assertion chjcli ⊢ A ∨ ℋ B ∈ C ℋ

Proof

Step Hyp Ref Expression
1 ch0le.1 ⊢ A ∈ C ℋ
2 chjcl.2 ⊢ B ∈ C ℋ
3 1 chshii ⊢ A ∈ S ℋ
4 2 chshii ⊢ B ∈ S ℋ
5 3 4 shjcli ⊢ A ∨ ℋ B ∈ C ℋ