theorem Th37:
  PSym(q,PSym(p,PSym(q,a))) = PSym(PSym(q,p),a)
proof
  Mid PSym(q,a),p,PSym(p,PSym(q,a)) by Def4;
  then Mid PSym(q,PSym(q,a)),PSym(q,p),PSym(q,PSym(p,PSym(q,a))) by Th35;
  then PSym(q,PSym(p,PSym(q,a)))=PSym(PSym(q,p),PSym(q,PSym(q,a))) by Def4;
  hence thesis by Th29;
end;
