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Definition df-cnv 4276
 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 ∈ V and B ∈ V then (A◡𝑅B ↔ B𝑅A), as proven in brcnv 4441 (see df-br 3735 and df-rel 4275 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 A = {⟨x, y⟩ ∣ yAx}
Distinct variable group:   x,y,A

Detailed syntax breakdown of Definition df-cnv
StepHypRef Expression
1 cA . . 3 class A
21ccnv 4267 . 2 class A
3 vy . . . . 5 setvar y
43cv 1225 . . . 4 class y
5 vx . . . . 5 setvar x
65cv 1225 . . . 4 class x
74, 6, 1wbr 3734 . . 3 wff yAx
87, 5, 3copab 3787 . 2 class {⟨x, y⟩ ∣ yAx}
92, 8wceq 1226 1 wff A = {⟨x, y⟩ ∣ yAx}
 Colors of variables: wff set class This definition is referenced by:  cnvss  4431  elcnv  4435  nfcnv  4437  opelcnvg  4438  csbcnvg  4442  cnvco  4443  relcnv  4626  cnvi  4651  cnvun  4652  cnvin  4654  cnvcnv3  4693
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