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;
reserve S for non empty multiplicatively-closed Subset of R;
reserve u,v,w,x,y,z for Element of Frac(S);
reserve a, b, c for Element of Frac(S);
reserve x, y, z for Element of S~R;

theorem Th34:
  x*y = y*x
   proof
     consider a such that
A1:  x = Class(EqRel(S),a) by Th32;
     consider b such that
A2:  y = Class(EqRel(S),b) by Th32;
     x*y = Class(EqRel(S),a*b) by A1,A2,Th33
     .= Class(EqRel(S),b*a)  .= y*x by A1,A2,Th33;
     hence thesis;
   end;
