Theorem chjoi

Description: The join of a closed subspace and its orthocomplement. (Contributed by NM, 24-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ch0le.1	|- A e. CH
Assertion	chjoi	|- ( A vH ( _|_ ` A ) ) = ~H

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	|- A e. CH
2	1	chssii	|- A C_ ~H
3		ssjo	|- ( A C_ ~H -> ( A vH ( _|_ ` A ) ) = ~H )
4	2 3	ax-mp	|- ( A vH ( _|_ ` A ) ) = ~H