Could anybody explain to me what's wrong with the following inference? Thanks.
$--- u$
$P(a)$
$---- {\forall}I^a$
$\forall x . P(x)$
$---- {\forall}E$
$P(b)$
$------ {\supset}I^u$
$P(a) \supset P(b)$
$-------- {\forall}I^b$
$\forall y . P(a) \supset P(b)$
$--------- {\forall}I^a$
$\forall x . \forall y . P(x) \supset P(y)$