I'm currently reading Artificial Intelligence, by Russel & Norvig. They state that:
A) A sentence is valid if it is true in all models
B) The deduction theorem: "For any sentences $\alpha$ and $\beta$, $\alpha \models \beta$ if and only if ($\alpha \implies \beta$) is valid.
My mental blockage consists of the fact that implication is False if $\alpha = T$ and $\beta = F$ -- thus resulting in one model that is not true. But, in order for ($\alpha \implies \beta$) to be valid, it has to be true for all models.
What is it I'm missing?