Past exam of the logic and set theory course of the University of Oxford / 2011 / A / 3 / b / i / Solution

The first-order term $t$ is free for substitution for $x_i$ in $\varphi$ if, at every free occurrence of $x_i$ to be replaced, no enclosing quantifier binds a variable occurring in $t$. Equivalently, the substitution introduces no variable capture. Only free occurrences of $x_i$ are replaced.