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 Th1:
    for a,b be Ideal of A, p be prime Ideal of A st a /\ b c= p holds
    a c= p or b c= p
    proof
      let a,b be Ideal of A, p be prime Ideal of A;
      assume
A1:   a /\ b c= p;
      a *' b c= a /\ b by IDEAL_1:79; then
      a *' b c= p by A1;
      hence thesis by TOPZARI1:30;
    end;
