Theorem ch0lei

Description: The closed subspace zero is the smallest member of CH . (Contributed by NM, 15-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ch0le.1	⊢ 𝐴 ∈ Cℋ
Assertion	ch0lei	⊢ 0ℋ ⊆ 𝐴

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	⊢ 𝐴 ∈ Cℋ
2		ch0le	⊢ ( 𝐴 ∈ Cℋ → 0ℋ ⊆ 𝐴 )
3	1 2	ax-mp	⊢ 0ℋ ⊆ 𝐴