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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 ∈ Cℋ
chjcl.2 ⊢ 𝐵 ∈ Cℋ
Assertion chub2i 𝐴 ⊆ ( 𝐵 ∨ℋ 𝐴 )

Proof

Step Hyp Ref Expression
1 ch0le.1 ⊢ 𝐴 ∈ Cℋ
2 chjcl.2 ⊢ 𝐵 ∈ Cℋ
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 )