A first-order quantifier $\forall x$ (also represented by $\text{Π}x$ by an analogy with a product) whose natural language equivalent is ‘for all $x$,…’. In classical logic, the truth condition for a universally quantified sentence $\forall x\phi (x)$ is that $\forall x\phi (x)$ is true in a model $M$ if every element of the domain of $M$ satisfies the formula $\phi (x)$, i.e., the propositional function corresponding to $\phi (x)$ maps each element of the domain to a designated value.