 reserve a for non empty set;
 reserve b, x, o for object;
reserve R for right_zeroed add-associative right_complementable Abelian
  well-unital distributive associative non trivial non trivial doubleLoopStr;
reserve R for non degenerated comRing;

theorem
    for R be non degenerated comRing holds
    ex X be Element of Polynom-Ring R st X is indeterminate & X = 1_1(R)
    proof
      let R be non degenerated comRing;
      reconsider X = 1_1(R) as Element of Polynom-Ring R
        by POLYNOM3:def 10;
A1:   (id Polynom-Ring R).1_1(R) = X;
      take X;
      thus thesis by A1;
    end;
