Are the two following formulations of the Axiom of Pairing in ZFC equivalent?
$$ \forall a, \forall b, \exists d: ~ \forall c ~(a \in d \wedge b \in d \wedge \neg (c \in d))$$
$$ \forall a, \forall b, \exists d: \forall c~ (c \in d \leftrightarrow c = a \vee c = b ) $$
I find the first formulation to be more elegant, since it does not use equality which would have to be defined before.
Thank you in advance!