Definition df-cnv 4002

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 3985	. 2 class `'A
3		vy	. . . . 5 set y
4	3	cv 1297	. . . 4 class y
5		vx	. . . . 5 set x
6	5	cv 1297	. . . 4 class x
7	4, 6, 1	wbr 3338	. . 3 wff yAx
8	7, 5, 3	copab 3395	. 2 class {<.x, y>. | yAx}
9	2, 8	wceq 1298	1 wff `'A = {<.x, y>. | yAx}

This definition is referenced by:  cnvss 4134  elcnv 4137  opelcnvg 4140  opelcnvgOLD 4141  cnvco 4145  cnvcoOLD 4146  relcnv 4301  cnvsymOLD 4305  cnvi 4320  cnvun 4322

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