 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 Th20:
  for G being unital non empty multMagma holds
    1_G is_a_unity_wrt the multF of G
proof
  let G be unital non empty multMagma;
  set o = the multF of G;
  now
    let h be Element of G;
    thus o.(1_G,h) = 1_G * h .= h by Def4;
    thus o.(h,1_G) = h * 1_G .= h by Def4;
  end;
  hence thesis by BINOP_1:3;
end;
