How can I represent that all element has some property?

Question

I want to represent mathematically that all elements $v \in V$ has $x$ and $y$ properties.

I tried:

Consider a graph $G=(V,E)$ where $\forall v \in V(G) \Rightarrow x[v] \in \mathbb{R} \space|\space y[v] \in \mathbb{R}$.

Is it correct?

Answer 1

If $x$ and $y$ are predicates with one variable each, then $\forall v\in V(G): x(v)\wedge y(v)$ or $\forall v: v\in V(G)\Rightarrow x(v)\wedge y(v)$.

Answer 2

As far as I know, there is no (standard) formal way to state explicitly that a variable "has such and such properties". Usually, this is simply explained or introduced in a "Notation" section.