Definition df-cnvrefs 36568

Description: Define the class of all converse reflexive sets, see the comment of df-ssr 36543. It is used only by df-cnvrefrels 36569. (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 36267	. 2 class CnvRefs
2		cid 5479	. . . . 5 class I
3		vx	. . . . . . . 8 setvar 𝑥
4	3	cv 1538	. . . . . . 7 class 𝑥
5	4	cdm 5580	. . . . . 6 class dom 𝑥
6	4	crn 5581	. . . . . 6 class ran 𝑥
7	5, 6	cxp 5578	. . . . 5 class (dom 𝑥 × ran 𝑥)
8	2, 7	cin 3882	. . . 4 class ( I ∩ (dom 𝑥 × ran 𝑥))
9	4, 7	cin 3882	. . . 4 class (𝑥 ∩ (dom 𝑥 × ran 𝑥))
10		cssr 36263	. . . . 5 class S
11	10	ccnv 5579	. . . 4 class ◡ S
12	8, 9, 11	wbr 5070	. . 3 wff ( I ∩ (dom 𝑥 × ran 𝑥))◡ S (𝑥 ∩ (dom 𝑥 × ran 𝑥))
13	12, 3	cab 2715	. 2 class {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥))◡ S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
14	1, 13	wceq 1539	1 wff CnvRefs = {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥))◡ S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}

This definition is referenced by:  dfcnvrefrels2  36571  dfcnvrefrels3  36572