Category:Universal Instantiation

This category contains pages concerning universal instantiation:

Suppose we have a universal statement:

$\forall x: \map P x$

where $\forall$ is the universal quantifier and $\map P x$ is a propositional function.

Then we can deduce:

$\map P {\mathbf a}$

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 $\mathbf a$.