 reserve R for commutative Ring;
 reserve A,B for non degenerated commutative Ring;
 reserve h for Function of A,B;
 reserve I0,I,I1,I2 for Ideal of A;
 reserve J,J1,J2 for proper Ideal of A;
 reserve p for prime Ideal of A;
 reserve S,S1 for non empty Subset of A;
 reserve E,E1,E2 for Subset of A;
 reserve a,b,f for Element of A;
 reserve n for Nat;
 reserve x,o,o1 for object;

theorem
  a is NonUnit of A implies ex m be maximal Ideal of A st a in m
  proof
    assume a is NonUnit of A; then
    {a}-Ideal <> [#] A by RING_2:20; then
    {a}-Ideal is proper; then
    consider m be maximal Ideal of A such that
A2: {a}-Ideal c= m by Th10;
    a in m by A2,IDEAL_1:66;
    hence thesis;
  end;
