 reserve K,F,E for Field,
         R,S for Ring;

theorem Th4:
   E is FieldExtension of F iff F is Subfield of E
   proof
A1:  now assume E is FieldExtension of F; then
       F is Subring of E by Def1;
       hence F is Subfield of E by RING_3:45;
     end;
     now assume F is Subfield of E; then
       F is Subring of E by RING_3:43;
       hence E is FieldExtension of F by Def1;
     end;
     hence thesis by A1;
   end;
