Notation for defining a set of distinct elements. Suppose I write the following.

Let $X = \{x,y,z\}.$

Then its pretty clear that what I really mean is the following.

Let $x,y$ and $z$ be fixed but arbitrary; suppose they're distinct; and let $X = \{x,y,z\}$.

Not that its really necessary or anything, but if there is an established convention for emphasizing that what I really mean is the second of these, then I'd like to start using it. Something like the following.

Let $X \equiv \{x,y,z\}.$

Does any such notational convention currently exist?

I think I've seen the notation $X=\{x,y,z\}_\ne$ used to indicate that $X$ is the set containing the distinct elements $x,y,z$; probably in some old paper by Erdős, Rado, and Hajnal, or some subset thereof. I know for a fact that the notation $\{x_0,x_1,\dots\}_\lt$ has been used to denote the set $\{x_0,x_1,\dots\}$ while expressing the fact that $x_0\lt x_1\lt\dots$; this notation is introduced on p. 428 of P. Erdős amd R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956), 427-489. Most likely the notation was Rado's invention. I don't know to what extent it has caught on.
I think Rado's(?) notation has the advantage over your $X\equiv\{x,y,z\}$ in that the meaning is easier to remember or guess; also you can simply write $\{x,y,z\}_\ne$ without necessarily having "$X=$" in front of it.
Update. Quoting from L. Mirsky, Transversal Theory, Academic Press, 1971, p. 2:

We shall use the symbol $\{x_1,\dots,x_k\}_\ne$ to denote the set consisting of the elements $x_1,\dots,x_k$ and at the same time express the fact that these elements are distinct. If the suffix '$\ne$' is not appended to the curly bracket, then no assumption is made about the distinctness of the elements listed.

