Theorem chex

Description: The set of closed subspaces of a Hilbert space exists (is a set). (Contributed by NM, 23-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Assertion	chex	$$⊢{\mathbf{C}}_{\mathscr{H}}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		shex	$$⊢{\mathbf{S}}_{\mathscr{H}}\in \mathrm{V}$$
2		chsssh	$$⊢{\mathbf{C}}_{\mathscr{H}}\subseteq {\mathbf{S}}_{\mathscr{H}}$$
3	1 2	ssexi	$$⊢{\mathbf{C}}_{\mathscr{H}}\in \mathrm{V}$$