Theorem hosubfni

Description: Functionality of difference of Hilbert space operators. (Contributed by NM, 2-Jun-2006) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hoeq.1	|- S : ~H --> ~H
	hoeq.2	|- T : ~H --> ~H
Assertion	hosubfni	|- ( 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	hosubcli	|- ( 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