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

theorem th1:
  a 'nand' b = 'not' (a '&' b)
proof
    let x be Element of Y;
    thus ('not' (a '&' b)).x = 'not' (a '&' b).x by MARGREL1:def 19
      .= 'not' (a.x '&' b.x) by MARGREL1:def 20
      .= 'not' ('not' (a.x 'nand' b.x)) by BVFUNC_1:46
      .= (a 'nand' b).x by Def3;
end;
