Symbols: If but not only if I was searching for a Latex symbol that indicates $A \Rightarrow B$ and $A \not\Leftarrow B$ ($B$ if not only if $A$, $B$ ifnf $A$). I thought of using $A \Leftrightarrow B$ with the left arrow tick < crossed out. Since I did not find such a symbol:
Is there a Latex symbol for this?
How common or understandable is this symbol?
If it isn't common: How easily is it confused with the symbol $\not\Leftrightarrow$?

Update: 
I need it for a sequence $A$ ifnf $B$ ifnf $C$ ifnf $D$, which I find more understandable than $A \Leftarrow B \Leftarrow C \Leftarrow D$  and $A \not\Rightarrow B \not\Rightarrow C \not\Rightarrow D$.
Of course I will prove both directions.
 A: When people assert implications, they often implicitly involve universal quantification.  For example, "if $n$ is a prime number greater than $2$, then $n$ is odd" really means "for all integers $n$, if $\dots$."  When one denies an implication, one includes the universal quantifier in the denial, so it becomes an existential quantifier.  For example, if someone says that "$n$ is odd" doesn't imply "$n$ is a prime number greater than $2$", he normally means to deny that "for all $n$, if $n$ is odd then $n$ is a prime number greater than $2$"; equivalently, he means to assert that "there exists an odd $n$ that is not a prime number greater than $2$." (Recall from propositional logic that the negation of $B\implies A$ is equivalent to $B\land\neg A$.)  So your proposed combined connective, for implication in one direction and denial of implication in the other direction, will implicitly quantify the variables partly with universal quantifiers and partly with existential ones.  This looks to me like a recipe for confusion and therefore well worth avoiding.
If, by good fortune, your statements $A$ and $B$  don't involve variables, so these quantification issues don't arise, then there is a fairly easy answer to your question.  As I said above, the negation of $B\implies A$ is equivalent to $B\land\neg A$.  Furthermore, this formula already implies that $A\implies B$, so
$$
(A\implies B)\land\neg(B\implies A)
$$
is equivalent to $B\land\neg A$.  But remember, this use of propositional logic is legitimate only if your $A$ and $B$ don't involve any variables that are implicitly quantified in your implications.
A: It is doubtful that a symbol exists; I do not believe it is common usage.
Note that your situation is equivalent to "$A$ implies $B$, but $B$ does not imply $A$". There are many, many situations in mathematics when this is the case. For instance:

Independent random variables have zero correleation coefficient, but a zero correlation coefficient does not imply that the random variables are independent.

In fact, the distinction that $A \implies B$ does not imply that $B \implies A$ is so important that it is almost always best addressed with more than a basic symbolic representation. The reader demands to know why the converse does not hold! Examples of situations where the converse does not hold are almost always useful.
A: You need to be careful with this connective (in classical logic) because it doesn't let you play fast and loose with the scope of free variables the way that $\to$ and $\leftrightarrow$ do.
I think using words in your expression is probably the best way to go, since it doesn't require additional context to understand.
$$ \varphi \;\;\text{if but not only if}\;\; \psi $$
If you need a compact notation for a chain of these things, I would recommend using plain $<$, but also call out what you are doing explicitly and give a definition of $<$. Comparison chaining should be intuitive to readers without additional comment.
$$ \varphi_1 < \varphi_2 < \varphi_3 $$
$$ \text{where $\xi$ < $\psi$ if and only if 
the values of $\xi$ are a proper subset of the values of $\psi$ } $$
Also, if you can collect the things you are talking about into a class or set, then you can use the notation $\subsetneq$ or proper subset or proper subclass to denote the relationship you are interested in.
