# Definition:First Order Logic with Identity

## Definition

A system of first order logic with identity is a system of predicate logic with the following elements in its alphabet:

#### Connectives

 $\displaystyle \land$ $\displaystyle :$ the conjunction sign $\displaystyle \lor$ $\displaystyle :$ the disjunction sign $\displaystyle \implies$ $\displaystyle :$ the conditional sign $\displaystyle \iff$ $\displaystyle :$ the biconditional sign $\displaystyle \neg$ $\displaystyle :$ the negation sign

#### Quantifiers

 $\displaystyle \exists$ $\displaystyle :$ the existential quantifier sign $\displaystyle \forall$ $\displaystyle :$ the universal quantifier sign

#### Identity

 $\displaystyle =$ $\displaystyle :$ the equality sign