 reserve m,n for Nat;
 reserve i,j for Integer;
 reserve S for non empty multMagma;
 reserve r,r1,r2,s,s1,s2,t for Element of S;
 reserve G for Group-like non empty multMagma;
 reserve e,h for Element of G;
 reserve G for Group;
 reserve f,g,h for Element of G;
 reserve u for UnOp of G;

theorem
  ord 1_G = 1
proof
A1: for n st (1_G) |^ n = 1_G & n <> 0 holds 1 <= n by NAT_1:14;
  (not 1_G is being_of_order_0) & (1_G) |^ 1 = 1_G by Lm4;
  hence thesis by A1,Def11;
end;
