Theorem pjhcli

Description: Closure of a projection in Hilbert space. (Contributed by NM, 7-Oct-2000) (New usage is discouraged.)

	Ref	Expression
Hypothesis	pjcl.1	|- H e. CH
Assertion	pjhcli	|- ( A e. ~H -> ( ( projh ` H ) ` A ) e. ~H )

Proof

Step	Hyp	Ref	Expression
1		pjcl.1	|- H e. CH
2		pjhcl	|- ( ( H e. CH /\ A e. ~H ) -> ( ( projh ` H ) ` A ) e. ~H )
3	1 2	mpan	|- ( A e. ~H -> ( ( projh ` H ) ` A ) e. ~H )