Theorem chub2

Description: Hilbert lattice join is greater than or equal to its second argument. (Contributed by NM, 12-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	chub2	⊢ ( ( 𝐴 ∈ Cℋ ∧ 𝐵 ∈ Cℋ ) → 𝐴 ⊆ ( 𝐵 ∨ℋ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		chub1	⊢ ( ( 𝐴 ∈ Cℋ ∧ 𝐵 ∈ Cℋ ) → 𝐴 ⊆ ( 𝐴 ∨ℋ 𝐵 ) )
2		chjcom	⊢ ( ( 𝐴 ∈ Cℋ ∧ 𝐵 ∈ Cℋ ) → ( 𝐴 ∨ℋ 𝐵 ) = ( 𝐵 ∨ℋ 𝐴 ) )
3	1 2	sseqtrd	⊢ ( ( 𝐴 ∈ Cℋ ∧ 𝐵 ∈ Cℋ ) → 𝐴 ⊆ ( 𝐵 ∨ℋ 𝐴 ) )