Theorem 7.1 (Los Lemma). Assuming that:

$L$ a language
$φ$ an $L$ -formula
${(M_{j})}_{j \in J} = {(M_{j}, I_{j})}_{j \in J}$ a non-empty family of $L$ -structures
$U$ an ultrafilter on $J$
$M = (\prod_{j \in J} M_{j} ∕ U, I_{U})$

Then

φ (M) = [φ {(M_{j})}_{j \in J}] .