Proving a simple assertion in Propositional Logic 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.
Thanks
 A: You can think of the phrase "[insert something here] holds" as "[that same something] is [insert property here]". More concretely, "holds" in this context is a sort of expression that refers to some thing "holding true" or always having the property of being true.
So, when we say $\alpha \Rightarrow \beta$ holds, we mean that $\alpha \Rightarrow \beta$ is in fact true.
A: 
Definition :
$\Gamma$ - set of one or more sentences
$S_1$ - conjunction of the elements of $\Gamma$
$S_2$ - sentence
then :  $\Gamma  \models S_2$ iff $\lnot(S_1 \land \lnot S_2)$

First of all $\alpha$ cannot be notation of the set and the sentence at the same time . But if we define $\Gamma$ as :
$\Gamma=\{\alpha\}$ then we can ask whether : $\Gamma \models \beta \Leftrightarrow (\alpha \Rightarrow \beta)$
Now let us observe following case :
$\Gamma$$= $ $\{ $ S likes ice cream $\}$
$S_1=$ S likes ice cream
$S_2=$ S is a man
then $\Gamma$ doesn't entail $S_2$ because :
"S likes ice cream" and "S is not a man" are not logically inconsistent because they can both be true .
Therefore if $\Gamma=\{\alpha\}$ then assertion : $\Gamma \models \beta \Leftrightarrow (\alpha \Rightarrow \beta)$ isn't valid .
