reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem Th10:
  g c= f & f is one-to-one implies g is one-to-one
proof
  assume g c= f & f is one-to-one;
  then for x1,x2,y st [x1,y] in g & [x2,y] in g holds x1 = x2 by Th9;
  hence thesis by Th9;
end;
