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Definition df-refs 35909
 Description: Define the class of all reflexive sets. It is used only by df-refrels 35910. We use subset relation S (df-ssr 35897) here to be able to define converse reflexivity (df-cnvrefs 35922), see also the comment of df-ssr 35897. The elements of this class are not necessarily relations (versus df-refrels 35910). Note the similarity of the definitions df-refs 35909, df-syms 35937 and df-trs 35967, cf. comments of dfrefrels2 35912. (Contributed by Peter Mazsa, 19-Jul-2019.)
Assertion
Ref Expression
df-refs Refs = {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}

Detailed syntax breakdown of Definition df-refs
StepHypRef Expression
1 crefs 35616 . 2 class Refs
2 cid 5427 . . . . 5 class I
3 vx . . . . . . . 8 setvar 𝑥
43cv 1537 . . . . . . 7 class 𝑥
54cdm 5523 . . . . . 6 class dom 𝑥
64crn 5524 . . . . . 6 class ran 𝑥
75, 6cxp 5521 . . . . 5 class (dom 𝑥 × ran 𝑥)
82, 7cin 3883 . . . 4 class ( I ∩ (dom 𝑥 × ran 𝑥))
94, 7cin 3883 . . . 4 class (𝑥 ∩ (dom 𝑥 × ran 𝑥))
10 cssr 35615 . . . 4 class S
118, 9, 10wbr 5033 . . 3 wff ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))
1211, 3cab 2779 . 2 class {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
131, 12wceq 1538 1 wff Refs = {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
 Colors of variables: wff setvar class This definition is referenced by:  dfrefrels2  35912
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