Full Idea
The first clear proof of the consistency of the first order predicate logic is found in the 1928 book of Hilbert and Ackermann.
Gist of Idea
The first clear proof of the consistency of the first order predicate logic was in 1928
Source
report of Hilbert,D/Ackermann,W (Principles of Theoretical Logic [1928]) by Michal Walicki - Introduction to Mathematical Logic History E.2.1
Book Reference
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.35