---
tag: 9T8WK38ZK8
kind: statement
role: proposition
name: First-order theories with identity
sources:
  - wikipedia: en:3512103@r1374090027
    locator: Theory (mathematical logic), section First-order theories > First-order theories with identity
    note: adopted
    mention: wikipedia://en/3512103#RBZ3
    sections: [Statement]
inventory: [ZGFRKTBG1J]
---

## Statement

A first-order theory $\mathcal{QS}$ is a first-order theory with identity if $\mathcal{QS}$ includes the identity relation symbol "=" and the reflexivity and substitution axiom schemes for this symbol.