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Metamath Proof Explorer

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 ∈ C ℋ
chjcl.2 ⊢ B ∈ C ℋ
Assertion chub2i ⊢ A ⊆ B ∨ ℋ A

Proof

Step Hyp Ref Expression
1 ch0le.1 ⊢ A ∈ C ℋ
2 chjcl.2 ⊢ B ∈ C ℋ
3 1 2 chub1i ⊢ A ⊆ A ∨ ℋ B
4 1 2 chjcomi ⊢ A ∨ ℋ B = B ∨ ℋ A
5 3 4 sseqtri ⊢ A ⊆ B ∨ ℋ A