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It's predicate logic and I need to find a counterexample to disprove the follwowing claim

$(A \models \phi \implies A \models \psi) \implies A \models \phi \rightarrow \psi$

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    You will have to give us the definition of the satisfaction relation $(\models)$ and what do you require of $\phi,\psi$, as you can see from the answers and their comments: it is unclear.2012-07-05
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    In particular, there are multiple definitions of $\models$ in the literature. These all agree on sentences, but for formulas with free variables they differ. In particular, you can ask whether your system satisfies $(A \models \phi) \to (A \models (\forall x)\phi)$. Some do and some do not. Which textbook are you following in your class?2012-07-05

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