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Mirrors > Home > MPE Home > Th. List > df-cnv | Structured version Visualization version Unicode version |
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 5305 (see df-br 4654 and df-rel 5121 for more on relations). For example, (ex-cnv 27294). 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.) |
Ref | Expression |
---|---|
df-cnv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | 1 | ccnv 5113 | . 2 |
3 | vy | . . . . 5 | |
4 | 3 | cv 1482 | . . . 4 |
5 | vx | . . . . 5 | |
6 | 5 | cv 1482 | . . . 4 |
7 | 4, 6, 1 | wbr 4653 | . . 3 |
8 | 7, 5, 3 | copab 4712 | . 2 |
9 | 2, 8 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: cnvss 5294 cnvssOLD 5295 elcnv 5299 nfcnv 5301 opelcnvg 5302 csbcnv 5306 csbcnvgALT 5307 cnvco 5308 relcnv 5503 cnv0 5535 cnvi 5537 cnvun 5538 cnvcnv3 5582 |
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