Theorem hocofi

Description: Mapping of composition 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	hocofi	|- ( S o. T ) : ~H --> ~H

Proof

Step	Hyp	Ref	Expression
1		hoeq.1	|- S : ~H --> ~H
2		hoeq.2	|- T : ~H --> ~H
3		fco	|- ( ( S : ~H --> ~H /\ T : ~H --> ~H ) -> ( S o. T ) : ~H --> ~H )
4	1 2 3	mp2an	|- ( S o. T ) : ~H --> ~H