reserve R for commutative Ring;
reserve A for non degenerated commutative Ring;
reserve I,J,q for Ideal of A;
reserve p for prime Ideal of A;
reserve M,M1,M2 for Ideal of A/q;

theorem Th22:
    (canHom q)"M1 is Ideal of A
    proof
A1:   (canHom q)"M1 is add-closed by Th20;
A2:   (canHom q)"M1 is left-ideal by Th21;
A3:   (canHom q).0.A =  Class(EqRel(A,q),0.A) by RING_2:def 5
      .= 0.(A/q) by RING_1:def 6;
A4:   dom (canHom q) = the carrier of A by FUNCT_2:def 1;
      (canHom q).0.A in M1 by A3,IDEAL_1:2; then
      0.A in (canHom q)"M1 by A4,FUNCT_1:def 7;
      hence thesis by A1,A2;
    end;
