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Definition df-cnv 4353
 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 4518 (see df-br 3765 and df-rel 4352 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 4344 . 2 class 𝐴
3 vy . . . . 5 setvar 𝑦
43cv 1242 . . . 4 class 𝑦
5 vx . . . . 5 setvar 𝑥
65cv 1242 . . . 4 class 𝑥
74, 6, 1wbr 3764 . . 3 wff 𝑦𝐴𝑥
87, 5, 3copab 3817 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑦𝐴𝑥}
92, 8wceq 1243 1 wff 𝐴 = {⟨𝑥, 𝑦⟩ ∣ 𝑦𝐴𝑥}
 Colors of variables: wff set class This definition is referenced by:  cnvss  4508  elcnv  4512  nfcnv  4514  opelcnvg  4515  csbcnvg  4519  cnvco  4520  relcnv  4703  cnvi  4728  cnvun  4729  cnvin  4731  cnvcnv3  4770
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