Here I am just wondering if there is some generally accepted convention (or if I have if and only if backwards?)
Specifically, I often see things like "THM: $A$ iff $B$" and then "PF (if part): Assume $A$. Show that $B$ is true"
That is, I often see people calling the "if" part of "A iff B" $A\implies B$. But I thought $A$ if $B$ means $B\implies A$ ? (as in If B is true then A must be true)
I realize that "A iff B" implies "B iff A". So if people often take $A\implies B$ to be the "if part of "A iff B", does than mean that it is convention to prove "A iff B" as "B iff A", or are people just using confusing notation?
This is just an error. There is a natural tendency to think of $A\Rightarrow B$ as the "first part" of $A\Leftrightarrow B$, and also a natural tendency to think of "if" as the "first part" of "if and only if". Since these conflict, people sometimes erroneously identify which part of $A\Leftrightarrow B$ is "if" and which part is "only if".