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Definition df-cnv 4296
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  _V and  _V then  `' R  R, as proven in brcnv 4461 (see df-br 3756 and df-rel 4295 for more on relations). For example,  `' {  <. 2 , 6  >.,  <. 3 , 9  >. } = {  <. 6 , 2  >.,  <. 9 , 3  >. } . 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 4287 . 2  `'
3 vy . . . . 5  setvar
43cv 1241 . . . 4
5 vx . . . . 5  setvar
65cv 1241 . . . 4
74, 6, 1wbr 3755 . . 3
87, 5, 3copab 3808 . 2  { <. ,  >.  |  }
92, 8wceq 1242 1  `'  { <. , 
>.  |  }
Colors of variables: wff set class
This definition is referenced by:  cnvss  4451  elcnv  4455  nfcnv  4457  opelcnvg  4458  csbcnvg  4462  cnvco  4463  relcnv  4646  cnvi  4671  cnvun  4672  cnvin  4674  cnvcnv3  4713
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