/sci/ - Science & Math

What does that bar mean? The author never defined it. Honestly I don't really know what's going on with this bit:

Suppose [math]f_i \colon A_i \rightarrow Y[/math] is a function, [math]1 \le i,\ j \le n[/math], iff [eqn]f_i \vert A_i \cap A_j = f_j \vert A_i \cap A_j, 1 \le i,\ j \le n.[/eqn]
I'm having a weird parsing error, I can't see the sides of the "iff".