reserve m,n for Nat;
reserve i,j for Integer;
reserve S for non empty addMagma;
reserve r,r1,r2,s,s1,s2,t,t1,t2 for Element of S;
reserve G for addGroup-like non empty addMagma;
reserve e,h for Element of G;
reserve G for addGroup;
reserve f,g,h for Element of G;
reserve u for UnOp of G;

theorem
  ord h = 1 implies h = 0_G
proof
  assume
A1: ord h = 1;
  then not h is being_of_order_0 by Def11;
  then 1 * h = 0_G by A1,Def11;
  hence thesis by Th25;
end;
