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I need to show that this formula $$(\forall x(A \to B) \to (\forall x A\to \forall x B))$$ is true for all interpretation. Could you help me please?

Thank you!

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    What rules of inference do you have for your system? What axioms do you have? (stock reply often used on the philosophy forums, but it works rather well).2011-09-15
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    @Doug: If fara worded the question correctly, what matters is the definition of *interpretation in a model* being used, not the axioms and rules of inference.2011-09-15
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    Your statement is of the form $P \Rightarrow (Q \Rightarrow R)$. Try a proof by contradiction, i.e. assume that $P,Q$ holds, but $R$ doesn't hold, and show that you get a contradiction.2011-09-15
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    @Brian If he rigorously shows it, how he shows it depends on the rules of inference and axioms he has. If you have a formal proof of a formula, and the system comes as sound, then you do have the formula as true for all interpretations by soundness.2011-09-16
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    @Doug: The question *as phrased* is asking for a model-theoretic argument. It’s a question about semantics, not syntax.2011-09-16

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