$A\cong B$ then $Th(A)=Th(B)$

Question

question: $A\cong B$ then $Th(A)=Th(B)$

answer: $\phi \in Th(A)$ then $A\vDash \phi$ and $A\cong B$ so we have $B\vDash \phi$ then $\phi \in Th(B)$ and $Th(A)\subseteq Th(B)$ and we could prove $Th(B)\subseteq Th(A)$ and so $Th(A)=Th(B)$.

is this answer true?

Answer 1

Yes, you've given a complete argument.

One might argue that it's nicer to use proper sentences, not connecting them with a string of "and"s, but the essence is flawless.