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 Th24:
  a 'nand' (b 'imp' c) = ('not' a 'or' b) '&' 'not' (a '&' c)
proof
  thus a 'nand' (b 'imp' c) = 'not' (a '&' (b 'imp' c)) by th1
    .= 'not' (a '&' ('not' b 'or' c)) by BVFUNC_4:8
    .= 'not' ((a '&' 'not' b) 'or' (a '&' c)) by BVFUNC_1:12
    .= 'not' (a '&' 'not' b) '&' 'not' (a '&' c) by BVFUNC_1:13
    .= (('not' a) 'or' ('not' 'not' b)) '&' 'not' (a '&' c) by BVFUNC_1:14
    .= ('not' a 'or' b) '&' 'not' (a '&' c);
end;
