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Definition df-cnv 4852
Description: Define the converse of a class. Definition 9.12 of [Quine] p. 64. The converse of a binary relation swaps its arguments, i.e., if and then , as proven in brcnv 5026 (see df-br 4303 and df-rel 4851 for more on relations). For example, (ex-cnv 22254). We use Quine's breve accent (smile) notation. Like Quine, we use it as a prefix, which eliminates the need for parentheses. Many authors use the postfix superscript "to the minus one." "Converse" is Quine's terminology; some authors call it "inverse," especially when the argument is a function. (Contributed by NM, 4-Jul-1994.)
Assertion
Ref Expression
df-cnv
Distinct variable group:   , ,

Detailed syntax breakdown of Definition df-cnv
StepHypRef Expression
1 cA . . 3
21ccnv 4843 . 2
3 vy . . . . 5
43cv 1661 . . . 4
5 vx . . . . 5
65cv 1661 . . . 4
74, 6, 1wbr 4302 . . 3
87, 5, 3copab 4359 . 2
92, 8wceq 1662 1
Colors of variables: wff set class
This definition is referenced by:  cnvss  5016  elcnv  5020  nfcnv  5022  opelcnvg  5023  csbcnv  5027  csbcnvgOLD  5028  cnvco  5029  relcnv  5208  cnvi  5242  cnvun  5243  cnvcnv3  5286
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