Universal Instantiation/Informal Statement

Theorem
Suppose we have a universal statement:
 * $\forall x: P \left({x}\right)$

where $\forall$ is the universal quantifier and $P \left({x}\right)$ is a propositional function.

Then we can deduce:
 * $P \left({\mathbf a}\right)$

where $\mathbf a$ is any arbitrary object we care to choose in the universe of discourse.

In natural language:


 * Suppose $P$ is true of everything in the universe of discourse.


 * ''Let $\mathbf a$ be an element of the universe of discourse."


 * Then $P$ is true of $\mathbf a$.

In the language of symbolic logic: