Theorem ch0le

Description: The zero subspace is the smallest member of CH . (Contributed by NM, 14-Aug-2002) (New usage is discouraged.)

	Ref	Expression
Assertion	ch0le	⊢ ( 𝐴 ∈ Cℋ → 0ℋ ⊆ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		chsh	⊢ ( 𝐴 ∈ Cℋ → 𝐴 ∈ Sℋ )
2		sh0le	⊢ ( 𝐴 ∈ Sℋ → 0ℋ ⊆ 𝐴 )
3	1 2	syl	⊢ ( 𝐴 ∈ Cℋ → 0ℋ ⊆ 𝐴 )