Is there a symbol for "given" in mathematics?

Some common symbols used to express the notion of "given" or "such that" are the colon ":" and the vertical bar "|".

I guess your statement could then be rephrased as:

$x \in \{ f(n),\ n \in \mathbb{N}\ |\ f(n) = f(n-1) + f(n-2),\ f(0) = 0,\ f(1) = 1 \} $

You can read $$A \rightarrow B$$ as "$A$ implies $B$" and $$A \leftarrow B$$ as "$A$ if $B$" or "$A$ given $B$."

For example, the statement "$n! = 1$ given that $n=0$" can be written $$n! = 1 \leftarrow n=0.$$