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definability by formulas in first-order logic, e.g. as explained at https://en.wikipedia.org/wiki/Definable_set, or as in J. Robinson's first-order definition of the integers in the field of rationals

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In NBG (ZFC + classes) if $P$ nonempty predicate of classes must $P$ have definable solution?

Let $A, B, C..X, Y$ range over potentially proper classes in NBG set theory (or adding class quantification to ZFC in obvious way) and $x,y,z$ range over sets. Since I don't know the proper symbols …
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