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 Th53:
  a 'eqv' (b 'nand' c) = (a '&' 'not' (b '&' c)) 'or' ('not' a '&' b '&' c)
proof
  thus a 'eqv' (b 'nand' c) =a 'eqv' 'not' (b '&' c) by th1
    .=(a '&' 'not' (b '&' c)) 'or' ('not' a '&' 'not' 'not' (b '&' c)) by
BVFUNC_6:92
    .=(a '&' 'not' (b '&' c)) 'or' ('not' a '&' b '&' c) by BVFUNC_1:4;
end;
