Elementary equivalence of models I'm quite new to model theory, so please correct me if I'm using wrong terminology. I need help with an exercise from Smirnov's book "Varieties of algebras" (In Russian). 
Problem: Assume that a model $\mathfrak{B}$ satisfies  all formulas of the elementary theory $\mathcal{T}(\mathfrak{A})$ of a model $\mathfrak{A}$. Prove that these models are elementary equivalent.
I have no ideas concerning the proof of this statement. We know that $\mathcal{T}(\mathfrak{A}) \subseteq \mathcal{T}(\mathfrak{B})$ and we need to show the reverse inclusion. But I don't know how to proceed since this statement seems false to me (I suppose this is due to I'm thinking more in terms of universal algebra and identities but not model theory and first order language formulas). Any help will be appreciated. Thanks!

The theory $\mathcal{T}(\mathfrak{A})$ is complete, so the reverse inclusion is automatic.
