Edge of Tree is Bridge

Theorem

Let $T$ be a tree.

Let $e$ be an edge of $T$.

Then $e$ is a bridge of $T$.

Proof

From Condition for Edge to be Bridge, $e$ is a bridge if and only if $e$ does not lie on any circuit.

Since $T$ is a tree, there are no circuits in $T$.

The result follows.

$\blacksquare$