# Do axioms say “iff”? (or, is it “if”, or, “only if”). [duplicate]

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:

1. $F_x\rightarrow A_x$ (i.e. "If some object $x$ is a field, the it also satisfies the field axioms"), and,

2. $A_x\rightarrow F_x$ (i.e. "If some object $x$ satisfies the field axiom, then it is also a field").

## marked as duplicate by Stefan Perko, joriki, Community♦Jun 28 '16 at 11:12

• You example is more a definition: "a structure $\mathcal F$ is a Field iff it satisfy the field axioms". – Mauro ALLEGRANZA Jun 28 '16 at 10:35