reserve p,q for Rational;
reserve g,m,m1,m2,n,n1,n2 for Nat;
reserve i,i1,i2,j,j1,j2 for Integer;
reserve R for Ring, F for Field;

theorem Th43:
  for R,S,T being Ring
  st R,S are_isomorphic & S,T are_isomorphic holds R,T are_isomorphic
  proof
    let R,S,T be Ring;
    assume
A1: R,S are_isomorphic & S,T are_isomorphic;
    then consider f being Function of R,S such that
A2: f is isomorphism;
    consider g being Function of S,T such that
A3: g is isomorphism by A1;
    g*f is one-to-one onto by A2,A3,FUNCT_2:27;
    hence thesis by A2,A3;
  end;
