reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;

theorem
  a 'eqv' b = (a 'or' b) 'imp' (a '&' b)
proof
  thus (a 'or' b) 'imp' (a '&' b) =(a 'imp' (a '&' b)) '&' (b 'imp' (a '&' b))
  by BVFUNC_6:51
    .=(a 'imp' b) '&' (b 'imp' (a '&' b)) by Th4
    .=(a 'imp' b) '&' (b 'imp' a) by Th4
    .=a 'eqv' b by BVFUNC_4:7;
end;
