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Definition df-cnv 4927
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 5097 (see df-br 4244 and df-rel 4926 for more on relations). For example, ?Error: 2 , 6 >. , <. 3 , 9 >. } = { <. 6 , 2 >. , <. 9 , 3 >. } ^ This math symbol is not active (i.e. was not declared in this scope). `'{<.2,6>.,<.3,9>.}={<.6,2>.,<.9,3>.} (ex-cnv 21796). 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 4918 . 2
3 vy . . . . 5
43cv 1653 . . . 4
5 vx . . . . 5
65cv 1653 . . . 4
74, 6, 1wbr 4243 . . 3
87, 5, 3copab 4300 . 2
92, 8wceq 1654 1
Colors of variables: wff set class
This definition is referenced by:  cnvss  5087  elcnv  5091  nfcnv  5093  opelcnvg  5094  csbcnv  5098  csbcnvgOLD  5099  cnvco  5100  relcnv  5286  cnvi  5320  cnvun  5321  cnvcnv3  5364
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