### Abstract

This work is a formalization of the soundness and completeness of an
axiomatic system for first-order logic. The proof system is based on
System Q1 by Smullyan and the completeness proof follows his textbook
"First-Order Logic" (Springer-Verlag 1968). The completeness
proof is in the Henkin style where a consistent set is extended to a
maximal consistent set using Lindenbaum's construction and Henkin
witnesses are added during the construction to ensure saturation as
well. The resulting set is a Hintikka set which, by the model
existence theorem, is satisfiable in the Herbrand universe.

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