first-order_formulas

A list of some first-order formulas.

$R$ is a function	$\forall x\exists y(xRy)\mbox{ and }\forall x,y,z(xRy\mbox{ and }xRz\Longrightarrow y=z)$
$f$ is onto	$\forall y\exists x(f(x)=y)$