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But that is like a convention because there is no x to make TRUE the statement.

Sorry, can anyone just tell me what \(\rm P(x)\) stands for?

I do know that conditional is not equivalent to \(\rm if\cdots then\) statements.

Oh, I get it.

if you give x the value -1 you can say that the proposition is FALSE.

If \(x \in \emptyset\), we know that \(P(x)\) is true so the conditional is true.

So the statement is always true, and it is given in your original statement that it is true.

Two statements having the same truth tables are equivalent.

Then can I turn every universal quantification into an implication?

yes you can

generally speaking
\[\forall x \in X, P(x)\]
is equivalent to
\[(x \in X) \rightarrow P(x)\]