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

theorem
   for R being non degenerated Ring, S being RingExtension of R,
   a being Element of S holds Ext_eval(1_.(R),a) = 1.S
   proof
     let R be non degenerated Ring, S be RingExtension of R;
     let a be Element of S;
     R is Subring of S by Def1;
     hence thesis by ALGNUM_1:14;
   end;
