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Definition df-cnvrefs 38506
Description: Define the class of all converse reflexive sets, see the comment of df-ssr 38479. It is used only by df-cnvrefrels 38507. (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 38168 . 2 class CnvRefs
2 cid 5581 . . . . 5 class I
3 vx . . . . . . . 8 setvar 𝑥
43cv 1535 . . . . . . 7 class 𝑥
54cdm 5688 . . . . . 6 class dom 𝑥
64crn 5689 . . . . . 6 class ran 𝑥
75, 6cxp 5686 . . . . 5 class (dom 𝑥 × ran 𝑥)
82, 7cin 3961 . . . 4 class ( I ∩ (dom 𝑥 × ran 𝑥))
94, 7cin 3961 . . . 4 class (𝑥 ∩ (dom 𝑥 × ran 𝑥))
10 cssr 38164 . . . . 5 class S
1110ccnv 5687 . . . 4 class S
128, 9, 11wbr 5147 . . 3 wff ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))
1312, 3cab 2711 . 2 class {𝑥 ∣ ( I ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
141, 13wceq 1536 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  38509  dfcnvrefrels3  38510
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