reserve C for non empty set;
reserve GF for Field,
        V for VectSp of GF,
        v,u for Element of V,
        W for Subset of V;
reserve f,f1,f2,f3 for PartFunc of C,V;
reserve F,G for Field,
        V for VectSp of F,
        W for VectSp of G;
reserve f,f1,f2 for Function of V, W;
reserve x,h for Element of V;
reserve r,r1,r2 for Element of G;

theorem Th3:
  fD(f,h)/.x = f/.(x+h) - f/.x
proof
  dom f = the carrier of V by FUNCT_2:def 1;
  hence fD(f,h)/.x = f/.(x+h) - f/.x by Th01;
end;
