Theorem choccli

Description: Closure of CH orthocomplement. (Contributed by NM, 29-Jul-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	choccl.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	choccli	$$⊢\perp \left(A\right)\in {\mathbf{C}}_{\mathscr{H}}$$

Proof

Step	Hyp	Ref	Expression
1		choccl.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		choccl	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}\to \perp \left(A\right)\in {\mathbf{C}}_{\mathscr{H}}$$
3	1 2	ax-mp	$$⊢\perp \left(A\right)\in {\mathbf{C}}_{\mathscr{H}}$$