A strengthened form of the variable sharing property in relevant logics demanding that variable sharing occur at a particular depth. To more precisely define the depth of an occurrence of an atomic formula in another formula as follows. Let $p$ be an instance of an atomic formula, then,

• • $p$ has depth $0$ in $p$

• • If $p$ has depth $n$ in the formula $\phi$, then $p$ has depth $n$ in $\neg \phi$, $\phi \circ \psi$, $\psi \circ \phi$ for $\circ \in \left\{\wedge ,\vee \right\}$

• • If $p$ has depth $n$ in the formula $\phi$, then $p$ has depth $n+1$ in $\phi \to \psi$ and $\psi \to \phi$

Effectively, depth is a measure of the number of conditional connectives within which a formula is nested. A deductive system $\text{L}$ satisfies the depth relevance condition if whenever $\phi \to \psi$ is an $\text{L}$-theorem, then there exists an instance $p$ of some atomic formula and a natural number $n$ such that $p$ has depth $n$ in both $\phi$ and $\psi$.