let X be non empty set ; for Y being ComplexNormSpace holds C_NormSpace_of_BoundedFunctions X,Y is ComplexNormSpace
let Y be ComplexNormSpace; C_NormSpace_of_BoundedFunctions X,Y is ComplexNormSpace
CLSStruct(# (ComplexBoundedFunctions X,Y),(Zero_ (ComplexBoundedFunctions X,Y),(ComplexVectSpace X,Y)),(Add_ (ComplexBoundedFunctions X,Y),(ComplexVectSpace X,Y)),(Mult_ (ComplexBoundedFunctions X,Y),(ComplexVectSpace X,Y)) #) is ComplexLinearSpace
;
hence
C_NormSpace_of_BoundedFunctions X,Y is ComplexNormSpace
by Th26, CSSPACE3:4; verum