  We provide short and simple proofs of the continuous time ballot theorem for
processes with cyclically interchangeable increments and Kendall's identity for
spectrally positive L\'evy processes. We obtain the later result as a direct
consequence of the former. The ballot theorem is extended to processes having
possible negative jumps. Then we prove through straightforward arguments based
on the law of bridges and Kendall's identity, Theorem 2.4 in \cite{mpp} which
gives an expression for the law of the supremum of spectrally positive L\'evy
processes. An analogous formula is obtained for the supremum of spectrally
negative L\'evy processes.
