reserve m,n for Nat;
reserve r for Real;
reserve c for Element of F_Complex;

theorem Th7:
  for R being Ring, S being Subring of R
  for x being Element of S holds x is Element of R
  proof
    let R be Ring;
    let S be Subring of R;
    let x be Element of S;
    the carrier of S c= the carrier of R by C0SP1:def 3;
    hence x is Element of R;
  end;
