This question already has an answer here:
My guess is that they say "iff", but I wanted to make sure as math books have never made it explicit.
To take the field axioms for example, is it fair to say that it says both:
$F_x\rightarrow A_x$ (i.e. "If some object $x$ is a field, the it also satisfies the field axioms"), and,
$A_x\rightarrow F_x$ (i.e. "If some object $x$ satisfies the field axiom, then it is also a field").