Theorem choccli

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

	Ref	Expression
Hypothesis	choccl.1	⊢ 𝐴 ∈ Cℋ
Assertion	choccli	⊢ ( ⊥ ‘ 𝐴 ) ∈ Cℋ

Proof

Step	Hyp	Ref	Expression
1		choccl.1	⊢ 𝐴 ∈ Cℋ
2		choccl	⊢ ( 𝐴 ∈ Cℋ → ( ⊥ ‘ 𝐴 ) ∈ Cℋ )
3	1 2	ax-mp	⊢ ( ⊥ ‘ 𝐴 ) ∈ Cℋ