let R, S, T be Ring; :: thesis: ( R,S are_isomorphic & S,T are_isomorphic implies R,T are_isomorphic )
assume A1: ( R,S are_isomorphic & S,T are_isomorphic ) ; :: thesis: R,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 & g * f is onto ) by A2, A3, FUNCT_2:27;
hence R,T are_isomorphic by A2, A3; :: thesis: verum