Is this the correct way to prove if and only if type of propositions?

Question

Suppose I have the proposition:

An object satisfies A if and only if B

Is this the following way to prove this?

$(\Rightarrow)$ If direction. Assume B is true, show A

$(\Leftarrow)$ only if direction. Assume A is true, show B

There seems a bit of reversal of logic I can't wrap my head around after waking up. Short term memoryloss perhaps.

Answer 1

You are right with what you say. Basically:

$$A\iff B \sim (A\implies B)\wedge (B\implies A)$$

So the best way to understand how to properly prove a iff is that you have to prove both directions, either in a direct way, by contrapositive or contradiction, depending strictly on the case.