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Metamath Proof Explorer

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	$⊢ A \in C_{ℋ} \to 0_{ℋ} \subseteq A$

Step	Hyp	Ref	Expression
1		chsh	$⊢ A \in C_{ℋ} \to A \in S_{ℋ}$
2		sh0le	$⊢ A \in S_{ℋ} \to 0_{ℋ} \subseteq A$
3	1 2	syl	$⊢ A \in C_{ℋ} \to 0_{ℋ} \subseteq A$