Interpretation An interpretation I of F is , where D is a non-empty set called the domain of individuals. I0 is a mapping defined on the constants of F satisfying 1. If c is an individual constant, then I0(c) ∈ D. 2. If f n is an n-ary function constant, then I0(f n) : Dn → D
Substitutivity of Equivalence Let A,M and N be wffs and let AMN be the result of replacing M by N at zero or more occurrences (henceforth called designate occurrences) of M in A. 1. AMN is a wff. 2. If |= M ≡ N then |= A ≡ AMN