This is the text from my book:
To define a statement $A$ so that it is true whenever the statement $B$ is true, we write $$A :\Leftrightarrow B$$ and say '$A$ is true, by definition, if $B$ is true'.
I don't quite understand it. How does it differ from $A := B$ or $A \Leftrightarrow B$? Please provide some examples if you can? Thanks in advance.
Just to check whether I have really understood this notation, is it correct to write $(X \subseteq Y) :\Leftrightarrow (\forall x \in X (x \in Y))$?