reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve C for Category;
reserve O for non empty Subset of the carrier of C;
reserve G,H for AddGroup;

theorem Th10:
  for f being strict GroupMorphismStr st dom(f) = G & cod(f) = H &
  fun(f) is additive holds f is strict Morphism of G,H
proof
  let f be strict GroupMorphismStr;
  assume that
A1: dom(f) = G & cod(f) = H and
A2: fun(f) is additive;
  reconsider f9 = f as strict GroupMorphism by A2,Def11;
  f9 is strict Morphism of G,H by A1,Def12;
  hence thesis;
end;
