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Definition df-cnvrefs 37033
Description: Define the class of all converse reflexive sets, see the comment of df-ssr 37006. It is used only by df-cnvrefrels 37034. (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
StepHypRef Expression
1 ccnvrefs 36687 . 2 class CnvRefs
2 cid 5531 . . . . 5 class I
3 vx . . . . . . . 8 setvar 𝑥
43cv 1541 . . . . . . 7 class 𝑥
54cdm 5634 . . . . . 6 class dom 𝑥
64crn 5635 . . . . . 6 class ran 𝑥
75, 6cxp 5632 . . . . 5 class (dom 𝑥 × ran 𝑥)
82, 7cin 3910 . . . 4 class ( I ∩ (dom 𝑥 × ran 𝑥))
94, 7cin 3910 . . . 4 class (𝑥 ∩ (dom 𝑥 × ran 𝑥))
10 cssr 36683 . . . . 5 class S
1110ccnv 5633 . . . 4 class S
128, 9, 11wbr 5106 . . 3 wff ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))
1312, 3cab 2710 . 2 class {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
141, 13wceq 1542 1 wff CnvRefs = {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
Colors of variables: wff setvar class
This definition is referenced by:  dfcnvrefrels2  37036  dfcnvrefrels3  37037
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