Definition df-cnv 4135

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 4118	. 2 class `'A
3		vy	. . . . 5 set y
4	3	cv 1585	. . . 4 class y
5		vx	. . . . 5 set x
6	5	cv 1585	. . . 4 class x
7	4, 6, 1	wbr 3507	. . 3 wff yAx
8	7, 5, 3	copab 3565	. 2 class {<.x, y>. | yAx}
9	2, 8	wceq 1586	1 wff `'A = {<.x, y>. | yAx}

This definition is referenced by:  cnvss 4262  elcnv 4265  opelcnvg 4268  cnvco 4272  relcnv 4419  cnvi 4431  cnvun 4432

Copyright terms: Public domain