Who first discovered the concept corresponding to the symbol of class comprehension 
 $\{x/\varphi\}$ used today in set theory ?



Who first discovered the concept corresponding to the symbol of class comprehension?
The concept is found with different notation in **Peano** ([1894](//zbmath.org/?q=an:25.0103.03), p. 20) (translated):



> 
> Let $p\_x$ be a proposition containing a variable letter $x$, that is, a condition on $x$. By the notation $\overline{x\ \varepsilon}\,p\_x$ we shall indicate the class of those $x$ that satisfy the condition $p\_x$.
> 
> 
> 


Von Neumann ([1923](//zbmath.org/?q=an:49.0139.02), Einleitung) uses $M$ for *Menge*:



> 
> Let $E(x)$ be a property, $f(x)$ a function defined for all $x$ possessing the property $E(x)$. Then
>  $$
> M(f(x); E(x))
> $$
>  shall be the set of all $f(x)$ as $x$ runs over all $x$ possessing the property $E(x)$.
> 
> 
> 


Our *notation* $\{\ ..\mid\,...\}$ is in e.g. **Lefschetz** ([1942](//ams.org/mathscinet-getitem?mr=7093), p. 2; [1949](//ams.org/mathscinet-getitem?mr=31708), p. 26; ...), Iwasawa ([1945](//ams.org/mathscinet-getitem?mr=31772); [1949](//mathscinet.ams.org/mathscinet-getitem?mr=29911); ...), Segal ([1946](//ams.org/mathscinet-getitem?mr=19218); [1947](//ams.org/mathscinet-getitem?mr=19617); ...), Kelley ([1947](//ams.org/mathscinet-getitem?mr=22999); [1953](//ams.org/mathscinet-getitem?mr=54175); [1955](//ams.org/mathscinet-getitem?mr=70144)), Mostow ([1949](//ams.org/mathscinet-getitem?mr=32656); [1950](//ams.org/mathscinet-getitem?mr=48464); ...), Yamabe ([1950](//ams.org/mathscinet-getitem?mr=36766)), Nomizu ([1950](//ams.org/mathscinet-getitem?mr=38354); [1954](//ams.org/mathscinet-getitem?mr=64057); ...), Godement ([1952](//ams.org/mathscinet-getitem?mr=44529); ...), Loomis ([1953](//ams.org/mathscinet-getitem?mr=54173); ...), etc. Kelley ([1947](//ams.org/mathscinet-getitem?mr=21315), p. 683) seems to attribute it to Lefschetz; Bernays ([1958](https://ams.org/mathscinet-getitem?mr=106178), § I.1) writes:



> 
> Our logical symbols are (...)
> 
> 
> 3) The class operator $\{\mathfrak r\mid\mathfrak{A(r)}\}$1)  « the class of the $\mathfrak r$ such that $\mathfrak{A(r)}$ » 
> 
> 
> (...)
> 
> 
> The rules concerning the class terms are: the formula schema (“Church schema”)
>  $$
> c\in\{\mathfrak r\mid\mathfrak{A(r)}\}\ \leftrightarrow\ \mathfrak A(c),
> $$
>  expressing a conversion law, in the sense of A. Church ([1932](//ams.org/mathscinet-getitem?mr=1503059)), and (...)
> 
> 
> 
> 
> ---
> 
> 
> 1) This symbol (used in some newer papers) is here taken, for the sake of easier print, instead of Russell’s class symbol $\hat{\mathfrak r}\mathfrak{A(r)}$, whose adoption was first intended.
> 
> 
> 




---


Added: Bernays’ *name* ***class operator*** for $\{\ ..\mid\,...\}$ came after Kelley’s ***classifier*** ([1955](//ams.org/mathscinet-getitem?mr=70144), p. 251); [***set-builder***](//hsm.stackexchange.com/questions/11026/where-did-the-term-set-builder-notation-come-from) seems to originate earlier in collective program books like *Universal Mathematics* ([1955](//babel.hathitrust.org/cgi/pt?u=1&id=mdp.39015017411003&seq=26), p. I-9), *Concepts and Structure of Mathematics* ([1954](//books.google.com/books?id=juRQAQAAMAAJ&q=%22set+builder%22), p. 117) and *Fundamental Mathematics* ([1948](//books.google.com/books?id=aUE_AQAAIAAJ&q=%22the+set-builder%22), p. 24) — the latter however using the different notation $\underset{\textstyle{..}}{\mathrm S}\,...$


