Axiom of Pairing. Given two sets $C$ and $D$, there is one set $X$ whose members are exactly $C$ and $D$. In symbols (which I hate them):
$$ \forall C,D\; \exists X : \forall x\, (x\in X \Longleftrightarrow x=C \mbox{ or } x=D). $$
If Wiki is right, this Axiom can be deduced either from the axiom of empty set and the axiom of power set or from the axiom of infinity. So in some sense, my question is stupid.
Anyway, is the following statement equivalent to the Axiom of pairing?:
My Statement. If $X$ and $Y$ are sets, then $X\cup Y$ is also a set.
Obviusly, it is not my idea, it is said by the book I'm following. The set of axioms the author uses is very similar to MK I think, but he considers this new axiom instead of the usual Axiom of Pairing and he doesn't consider the Axiom of Empty set (but he considers the Axiom of Infinite, so it doesn't matter).
Thanks.
My book follows EXACTLY (with the same names) the axioms in Kelly's General toplogy (see here). Moreover, Wiki says ''Kelly introduced his axioms gradually, as needed to develop the topics listed after each instance of Develop below'', and the same happens with the author of my book. So probably my next question will be about Kelly's General Topology...