reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;
reserve o,m for set;
reserve B,C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,f1,f2,g,g1,g2 for Morphism of C;
reserve f,f1,f2 for Morphism of a,b;
reserve f9 for Morphism of b,a;
reserve g for Morphism of b,c;
reserve h,h1,h2 for Morphism of c,d;

theorem
  id b is epi
proof
A1: now
    let c;
    let g1,g2 be Morphism of b,c;
    assume
A2: Hom(b,c)<>{};
    then g1*(id b) = g1 by Th24;
    hence g1*(id b) = g2*(id b) implies g1 = g2 by A2,Th24;
  end;
  thus thesis by A1;
end;
