I have to prove some Propositional Logic assertions.
Given this one: $\alpha \models \beta \Leftrightarrow (\alpha \Rightarrow \beta)$ is valid
Where $\models$ is entailment
The answer is: $\alpha \Rightarrow \beta$ holds in those models where $\beta$ holds or where $\neg\alpha$ holds. This is precisely the case if $\alpha \Rightarrow \beta$ is valid.
I don't understand this answer. Could someone clarify it for me. I don't know what holds means in this context. English is not my first language.
I know that a sentence to be valid needs to be True in all models. Also that $\alpha \models \beta \Leftrightarrow$ in every model in which $\alpha$ is true, $\beta$ is also true.