A syntactic or semantic consequence relation $⊢$ that is closed under uniform substitutions, that is, where $\text{Γ}\cup \left\{\psi \right\}$ is a set of formulae, if

• • $\text{Γ}⊢\psi$

then the following holds:

• • $\left\{\phi \left[\xi /p\right]\mid \phi \in \text{Γ}\right\}⊢\psi \left[\xi /p\right]$

where $\zeta \left[\xi /p\right]$ is the formula that results from uniformly replacing instances of the atom $p$ with the formula $\xi$.