Universal Quantifier

$\forall x:P(x)\equiv P(x_1)\wedge P(x_2)\wedge \dots P(x_n)\wedge \dots$

• $P(x)$ is a predicate
• The truth value of the statement “for all x such that $P(x)$ is true” is the same as $P(x_1)$ is true and $P(x_n)$ for all other $n$ is true