Description: An orthogonal complement is a subset of Hilbert space. (Contributed by NM, 9-Aug-2000) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | ocss | ⊢ ( 𝐴 ⊆ ℋ → ( ⊥ ‘ 𝐴 ) ⊆ ℋ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ocsh | ⊢ ( 𝐴 ⊆ ℋ → ( ⊥ ‘ 𝐴 ) ∈ Sℋ ) | |
2 | shss | ⊢ ( ( ⊥ ‘ 𝐴 ) ∈ Sℋ → ( ⊥ ‘ 𝐴 ) ⊆ ℋ ) | |
3 | 1 2 | syl | ⊢ ( 𝐴 ⊆ ℋ → ( ⊥ ‘ 𝐴 ) ⊆ ℋ ) |