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 Th46:
   for z holds
   ex r1,r2 be Element of R st r2 in S & z = Class(EqRel(S),[r1,r2])
   proof
     let z;
     consider r be Element of Frac(S)  such that
A1:  z = Class(EqRel(S),r) by Th32;
     consider r1,r2 be Element of R such that
A2:  r1 = r`1 and
A3:  r2 = r`2;
     z = Class(EqRel(S),[r1,r2]) by A1,A2,A3;
     hence thesis by A3,Lm17;
   end;
