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 )