Metamath Proof Explorer


Theorem shss

Description: A subspace is a subset of Hilbert space. (Contributed by NM, 9-Oct-1999) (Revised by Mario Carneiro, 23-Dec-2013) (New usage is discouraged.)

Ref Expression
Assertion shss HSH

Proof

Step Hyp Ref Expression
1 issh HSH0H+H×HH×HH
2 1 simplbi HSH0H
3 2 simpld HSH