reserve G for strict Group,
  a,b,x,y,z for Element of G,
  H,K for strict Subgroup of G,
  p for Element of NAT,
  A for Subset of G;

theorem
  for G being strict finite Group holds
  p is prime & card G = p implies ex a being Element of G st ord a = p
proof
  let G be strict finite Group;
  assume that
A1: p is prime and
A2: card G = p;
  G is cyclic Group by A1,A2,GR_CY_1:21;
  hence thesis by A2,GR_CY_1:19;
end;
