reserve a,b,c,d,x,y,z for object, X,Y,Z for set;
reserve R,S,T for Relation;
reserve F,G for Function;

theorem Th36:
  F is_isomorphism_of R,S implies for a,b st [a,b] in R & a <> b
  holds [F.a,F.b] in S & F.a <> F.b
proof
  assume
A1: F is_isomorphism_of R,S;
  then
A2: dom F = field R & F is one-to-one;
  let a,b;
  assume that
A3: [a,b] in R and
A4: a <> b;
  a in field R & b in field R by A1,A3;
  hence thesis by A1,A2,A3,A4;
end;
