Definition df-cnvrefs 37390

Description: Define the class of all converse reflexive sets, see the comment of df-ssr 37363. It is used only by df-cnvrefrels 37391. (Contributed by Peter Mazsa, 22-Jul-2019.)

Assertion

Ref	Expression
df-cnvrefs	⊢ CnvRefs = {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥))◡ S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}

Detailed syntax breakdown of Definition df-cnvrefs

Step	Hyp	Ref	Expression
1		ccnvrefs 37045	. 2 class CnvRefs
2		cid 5573	. . . . 5 class I
3		vx	. . . . . . . 8 setvar 𝑥
4	3	cv 1540	. . . . . . 7 class 𝑥
5	4	cdm 5676	. . . . . 6 class dom 𝑥
6	4	crn 5677	. . . . . 6 class ran 𝑥
7	5, 6	cxp 5674	. . . . 5 class (dom 𝑥 × ran 𝑥)
8	2, 7	cin 3947	. . . 4 class ( I ∩ (dom 𝑥 × ran 𝑥))
9	4, 7	cin 3947	. . . 4 class (𝑥 ∩ (dom 𝑥 × ran 𝑥))
10		cssr 37041	. . . . 5 class S
11	10	ccnv 5675	. . . 4 class ◡ S
12	8, 9, 11	wbr 5148	. . 3 wff ( I ∩ (dom 𝑥 × ran 𝑥))◡ S (𝑥 ∩ (dom 𝑥 × ran 𝑥))
13	12, 3	cab 2709	. 2 class {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥))◡ S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
14	1, 13	wceq 1541	1 wff CnvRefs = {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥))◡ S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}

This definition is referenced by:  dfcnvrefrels2  37393  dfcnvrefrels3  37394