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By applying a state-of-the-art angle-resolved photoemission to LiFeAs, the only stoichiometric pnictide superconductor without magnetic ordering, we identify a clear fingerprint of the phonon spectrum in the fermionic self-energy and estimate the electron-phonon coupling strength, which appears to be sufficient to mediate the superconductivity. This result suggests that the superconductivity in pnictides could be based on the conventional phonon pairing enhanced by the van Hove singularity in the electronic density of states and by the strong electron-electron interaction.