reserve R,R1 for commutative Ring;
reserve A,B for non degenerated commutative Ring;
reserve o,o1,o2 for object;
reserve r,r1,r2 for Element of R;
reserve a,a1,a2,b,b1 for Element of A;
reserve f for Function of R, R1;
reserve p for Element of Spectrum A;

theorem Th5:
  {1.R} is multiplicatively-closed
  proof
    set M = {1.R};
    for r1,r2 be Element of R st r1 in M & r2 in M holds r1 * r2 in M
    proof
      let r1,r2 be Element of R;
      assume
A2:   r1 in M & r2 in M; then
      r1 * r2 = 1.R * r1 by TARSKI:def 1 .= 1.R by A2, TARSKI:def 1;
      hence thesis by TARSKI:def 1;
    end;
    hence thesis by TARSKI:def 1;
  end;
