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
  a 'nand' (b 'xor' c) = (a '&' b) 'eqv' (a '&' c)
proof
  thus a 'nand' (b 'xor' c) = 'not' (a '&' (b 'xor' c)) by th1
    .= 'not' ((a '&' b) 'xor' (a '&' c)) by Th11
    .= 'not' 'not' ((a '&' b) 'eqv' (a '&' c)) by BVFUNC_6:85
    .= (a '&' b) 'eqv' (a '&' c);
end;
