Parsons has given a (nonconstructive) proof that the first-order fragment of the system of Frege's Grundgesetze is consistent. Here a constructive proof of the same result is presented.
"On a Consistent Subsystem of Frege's Grundgesetze." Notre Dame J. Formal Logic 39 (2) 274 - 278, Spring 1998. https://doi.org/10.1305/ndjfl/1039293068