\begin{definition}[Definition:Relativisation]
Let $p$ be a well-formed formula of the language of set theory.
Let $A$ be a class.
The '''relativisation of $p$ to $A$''' shall be denoted $p^A$ and shall be defined recursively on the symbols in $p$:
:$x \in y ^A \iff x \in y$
:$\left({\neg p}\right)^A \iff \neg p^A$
:$\left({p \land q}\right)^A \iff \left({p^A \land q^A}\right)$
:$\left({\forall x: P \left({x}\right)}\right)^A \iff \forall x: \left({ x \in A \implies P \left({x}\right)^A}\right)$
Thus, the relativisation of $p$ is simply the well-formed formula achieved when replacing all instances of $\forall x$ with $\forall x \in A$.
\end{definition}