Writing propositions using connectives and quantifiers

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So I have this statement that says:

For every two real numbers $x$ and $y$ with $x < y$, there is a real number with the property $P$ between $x$ and $y$.

Let $P(x)$ be the statement that says that a real number $x$ has some property $P$.

I have to write this using connectives and quantifiers and construct a negation for this proposition.

I've started by using the statements:

$(∀x \in R)(∀y \in R)(x < y)(x < P(x) < y)$

Something along the lines of this although I know this is incorrect.