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Metamath Proof Explorer

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 e. SH -> ( _|_ ` A ) C_ ~H )

Proof

Step Hyp Ref Expression
1 shss 
 |-  ( A e. SH -> A C_ ~H )
2 ocss 
 |-  ( A C_ ~H -> ( _|_ ` A ) C_ ~H )
3 1 2 syl 
 |-  ( A e. SH -> ( _|_ ` A ) C_ ~H )