Definition df-cnv 3267

Description: Define the converse of a class. Definition 9.12 of [Quine] p. 64. 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.

Assertion

Ref	Expression
df-cnv	⊢ ◡A = {<.x, y>.∣yAx}

Distinct variable group:   x,y,A

Detailed syntax breakdown of Definition df-cnv

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	ccnv 3250	. 2 class ◡A
3		vy	. . . . 5 set y
4	3	cv 991	. . . 4 class y
5		vx	. . . . 5 set x
6	5	cv 991	. . . 4 class x
7	4, 6, 1	wbr 2692	. . 3 wff yAx
8	7, 5, 3	copab 2740	. 2 class {<.x, y>.∣yAx}
9	2, 8	wceq 992	1 wff ◡A = {<.x, y>.∣yAx}

This definition is referenced by:  cnvss 3381  elcnv 3384  opelcnvg 3387  cnvco 3391  relcnv 3527  cnvsym 3529

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