theorem Th70:
  for A, t, u st GRZ-axioms c= A & A, GRZ-rules |- t '=' u holds
      A, GRZ-rules |- u '=' t
proof
  let A, t, u;
  assume that
    A1: GRZ-axioms c= A and
    A2: A, GRZ-rules |- t '=' u;
  set v = (t '=' u) '=' (u '=' t);
  v in GRZ-axioms by Def10;
  then A, GRZ-rules |- v by A1, Th46;
  hence thesis by A2, Th61;
end;
