Theorem hoaddfni

Description: Functionality of sum of Hilbert space operators. (Contributed by NM, 14-Nov-2000) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hoeq.1	|- S : ~H --> ~H
	hoeq.2	|- T : ~H --> ~H
Assertion	hoaddfni	|- ( S +op T ) Fn ~H

Proof

Step	Hyp	Ref	Expression
1		hoeq.1	|- S : ~H --> ~H
2		hoeq.2	|- T : ~H --> ~H
3	1 2	hoaddcli	|- ( S +op T ) : ~H --> ~H
4		ffn	|- ( ( S +op T ) : ~H --> ~H -> ( S +op T ) Fn ~H )
5	3 4	ax-mp	|- ( S +op T ) Fn ~H