Metamath Proof Explorer


Theorem chocini

Description: Intersection of a closed subspace and its orthocomplement. Part of Proposition 1 of Kalmbach p. 65. (Contributed by NM, 11-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypothesis ch0le.1 A C
Assertion chocini A A = 0

Proof

Step Hyp Ref Expression
1 ch0le.1 A C
2 1 chshii A S
3 ocin A S A A = 0
4 2 3 ax-mp A A = 0