reserve C for CategoryStr;
reserve f,f1,f2,f3 for morphism of C;
reserve g1,g2 for morphism of C opp;
reserve C,D,E for with_identities CategoryStr;
reserve F for Functor of C,D;
reserve G for Functor of D,E;
reserve f for morphism of C;

theorem
  ex C,D being category, F being Functor of C,D st
  F is non multiplicative & F is identity-preserving
  proof
    set C = the non empty category;
    set D = the empty category;
    set F = the identity-preserving Functor of C,D;
    take C,D,F;
    thus thesis by Th29;
  end;
