Definition df-cnv 4786

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. (Contributed by SF, 5-Jan-2015.)

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 4772	. 2 class ◡A
3		vy	. . . . 5 setvar y
4	3	cv 1641	. . . 4 class y
5		vx	. . . . 5 setvar x
6	5	cv 1641	. . . 4 class x
7	4, 6, 1	wbr 4640	. . 3 wff yAx
8	7, 5, 3	copab 4623	. 2 class {⟨x, y⟩ ∣ yAx}
9	2, 8	wceq 1642	1 wff ◡A = {⟨x, y⟩ ∣ yAx}

This definition is referenced by:  cnvss  4886  elcnv  4890  nfcnv  4892  brcnv  4893  cnvco  4895  cnvi  5033  cnvun  5034