Theorem shocss

Description: An orthogonal complement is a subset of Hilbert space. (Contributed by NM, 11-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Assertion	shocss	⊢ ( 𝐴 ∈ Sℋ → ( ⊥ ‘ 𝐴 ) ⊆ ℋ )

Proof

Step	Hyp	Ref	Expression
1		shss	⊢ ( 𝐴 ∈ Sℋ → 𝐴 ⊆ ℋ )
2		ocss	⊢ ( 𝐴 ⊆ ℋ → ( ⊥ ‘ 𝐴 ) ⊆ ℋ )
3	1 2	syl	⊢ ( 𝐴 ∈ Sℋ → ( ⊥ ‘ 𝐴 ) ⊆ ℋ )