 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 h = 1 implies h = 1_G
proof
  assume
A1: ord h = 1;
  then not h is being_of_order_0 by Def11;
  then h |^ 1 = 1_G by A1,Def11;
  hence thesis by Th25;
end;
