is $P(x) \to \forall x P(x)$ satisfiable

Question

I need to prove that this formula $P(x) \to \forall x P(x)$ is satisfiable. Can I say for example that x is even number ?

Answer 1

If $P(x)$ is true for all $x$, then $\forall x P(x)$ and the implication is true.

If $P(x)$ if false for some $x=x_0$, then $P(x_0)\implies\forall x P(x)$ is true because $P(x_0)$ is false.