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	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	ch0lei	$$⊢0_{\mathscr{H}}\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		ch0le	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}\to 0_{\mathscr{H}}\subseteq A$$
3	1 2	ax-mp	$$⊢0_{\mathscr{H}}\subseteq A$$