MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-cnv Unicode version

Definition df-cnv 5012
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 5190 (see df-br 4453 and df-rel 5011 for more on relations). For example, (ex-cnv 25158). 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 5003 . 2
3 vy . . . . 5
43cv 1394 . . . 4
5 vx . . . . 5
65cv 1394 . . . 4
74, 6, 1wbr 4452 . . 3
87, 5, 3copab 4509 . 2
92, 8wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  cnvss  5180  elcnv  5184  nfcnv  5186  opelcnvg  5187  csbcnv  5191  csbcnvgALT  5192  cnvco  5193  relcnv  5379  cnvi  5415  cnvun  5416  cnvcnv3  5461
  Copyright terms: Public domain W3C validator