Theorem hlmulf

Description: Mapping for Hilbert space scalar multiplication. (Contributed by NM, 7-Sep-2007) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hlmulf.1	|- X = ( BaseSet ` U )
	hlmulf.4	|- S = ( .sOLD ` U )
Assertion	hlmulf	|- ( U e. CHilOLD -> S : ( CC X. X ) --> X )

Proof

Step	Hyp	Ref	Expression
1		hlmulf.1	|- X = ( BaseSet ` U )
2		hlmulf.4	|- S = ( .sOLD ` U )
3		hlnv	|- ( U e. CHilOLD -> U e. NrmCVec )
4	1 2	nvsf	|- ( U e. NrmCVec -> S : ( CC X. X ) --> X )
5	3 4	syl	|- ( U e. CHilOLD -> S : ( CC X. X ) --> X )