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Definition df-cnv 4697
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  A  e. 
_V and  B  e.  _V then  ( A `' R B  <-> 
B R A ), as proven in brcnv 4864 (see df-br 4024 and df-rel 4696 for more on relations). For example,  `' { <. 2 ,  6 >. , 
<. 3 ,  9
>. }  =  { <. 6 ,  2 >. , 
<. 9 ,  3
>. } (ex-cnv 20824). 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  |-  `' A  =  { <. x ,  y
>.  |  y A x }
Distinct variable group:    x, y, A

Detailed syntax breakdown of Definition df-cnv
StepHypRef Expression
1 cA . . 3  class  A
21ccnv 4688 . 2  class  `' A
3 vy . . . . 5  set  y
43cv 1622 . . . 4  class  y
5 vx . . . . 5  set  x
65cv 1622 . . . 4  class  x
74, 6, 1wbr 4023 . . 3  wff  y A x
87, 5, 3copab 4076 . 2  class  { <. x ,  y >.  |  y A x }
92, 8wceq 1623 1  wff  `' A  =  { <. x ,  y
>.  |  y A x }
Colors of variables: wff set class
This definition is referenced by:  cnvss  4854  elcnv  4858  nfcnv  4860  opelcnvg  4861  cnvco  4865  relcnv  5051  cnvi  5085  cnvun  5086  cnvcnv3  5123  csbcnvg  23198
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