Correct terms to refer the implications $\implies$ and $\impliedby$ in a "if and only if" statement. My writing a proof of a complex proposition of the type "$A \iff B$" for a paper.
I want to close a block of argumentation with a sentence like "Which concludes the first implication". Here I am calling the "$\implies$" as the first implication, but I don't know if this is the correct term to use.
What is the correct term to refer to the "$\implies$" and the "$\impliedby$" implication in the mentioned context?
 A: The $\implies$ direction is called sufficiency, and the $\impliedby$ direction is called necessity.
A: I would say something as: ($\dots$) which concludes the previous "if A, then B" statement.
Remark 1: From here on, we indicate the forward/direct implication as "$A \Rightarrow$ B", whereas we use "$A \Leftarrow$ B" for its opposite relation (i.e., a reverse relation between proposition A and proposition B).
A: @BrevanEllefsen answered in comments, $\Rightarrow$ is the forward implication while $\Leftarrow$ is the reverse implication.
In practice, I like @TheoBendit's suggestion of preceding the paragraph where you start proving one of the implications by $(\Rightarrow)$ or $(\Leftarrow)$ (with appropriate formatting like indent,...) very much, especially on my personal notes or drafts.
On the other hand, if your proof is well-constructed, this could be superfluous. Frame the proof of each implication by the necessary assumptions and conclusion ("Assume A. Then [...]. This implies that B") and separate the two proofs by "Conversely", or similar expressions.
