This question comes from my propositional calculus homework and I do not know where to start the proof.
Let $\Phi = \{A_1, A_2, ...\}$ be an infinite set of sentences. Suppose that for all $n$, $A_{n+1}$ is not a logical consequence of $\{A_1, ..., A_n\}$. Now let $B$ be any sentence such that $\Phi \models B$. Prove that there exists $n$ such that $A_n$ is not a logical consequence of $B$.
Help would be greatly appreciated.
As mentioned by Dan Thousand, if $\Phi \models B$, there is a finite subset $ \phi = \{A_1, A_2, \dots, A_N\}$ of $\Phi$ that models $B$. Then $A_{N+1}$ can't be a logical consequence of $B$ as otherwise it would be a logical consequence of $\phi$ in contradiction with one of our hypothesis.