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Definition df-cnv 4870
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 5044 (see df-br 4319 and df-rel 4869 for more on relations). For example, (ex-cnv 22766). 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 4861 . 2
3 vy . . . . 5
43cv 1669 . . . 4
5 vx . . . . 5
65cv 1669 . . . 4
74, 6, 1wbr 4318 . . 3
87, 5, 3copab 4375 . 2
92, 8wceq 1670 1
Colors of variables: wff set class
This definition is referenced by:  cnvss  5034  elcnv  5038  nfcnv  5040  opelcnvg  5041  csbcnv  5045  csbcnvgOLD  5046  cnvco  5047  relcnv  5229  cnvi  5263  cnvun  5264  cnvcnv3  5307
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