Full Idea
First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences.
Gist of Idea
First-order logic is 'compact': consequences of a set are consequences of a finite subset
Source
William D. Hart (The Evolution of Logic [2010], 3)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.80