Take the tour ×  $ \models \phi \to \forall x.\phi$ where $\phi$
is WFF and x not free in $\phi$  Does that render that $ \phi
\to \forall x.\phi$ is true in any cases?  share|improve this
question possible duplicate of How to prove this models. Note:
This is question 1(a) of this assignment sheet. –  Henning
Makholm Nov 16 '11 at 23:10 @Henning: I've closed the other one
as a duplicate of this one, just because this is the one with
the answer in it. –  Zev Chonoles Nov 18 '11 at 22:51 @Zev, it's
not clear that they are really duplicates -- the OP here seemed
to want to know what was being asked of him, whereas in the
other question wanted help actually doing it. But in any case
the question is now academic (!); the assignment was due
yesterday. (Hmm, I see now that the asker was the same. Didn't
notice that before). –  Henning Makholm Nov 18 '11 at 22:59 add
comment  1 Answer  up vote 1 down vote accepted  Yes,
$\vDash\psi$ means that $\psi$ is logically valid, that is, true
in every interpretation of the la