consider X being set such that
A1: for x being set holds
( x in X iff ( x in Funcs the carrier of V,the carrier of V & S₁[x] ) ) from XBOOLE_0:sch 1();
take X ; :: thesis: for x being set holds
( x in X iff x is onto isometric Function of V,V )
let x be set ; :: thesis: ( x in X iff x is onto isometric Function of V,V )
thus ( x in X implies x is onto isometric Function of V,V ) by A1; :: thesis: ( x is onto isometric Function of V,V implies x in X )
assume A2: x is onto isometric Function of V,V ; :: thesis: x in X
then x in Funcs the carrier of V,the carrier of V by FUNCT_2:11;
hence x in X by A1, A2; :: thesis: verum