For All

A Quantifier $\forall$ For all of a set. It is applied immediately to the free variable after, $\forall x$, rather than for the entire statement similar to how $\neg$ is only for a single term after

Make sure you write a comma after you use this in a Mathematical Statement. Example: $\forall x\in R,x^2{\ge }_0$

Proof Writing

$\forall x\in D,P(x)$ First let x be an arbitrary element of D, then prove $P(x)$ to be true

Distributive Law

$\forall$ is distributive for And $\forall xE(x)\wedge \forall xT(x)\equiv \forall x(E(x)\wedge T(x))$