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Definition df-syms 36089
 Description: Define the class of all symmetric sets. It is used only by df-symrels 36090. Note the similarity of the definitions df-refs 36061, df-syms 36089 and df-trs 36119, cf. the comment of dfrefrels2 36064. (Contributed by Peter Mazsa, 19-Jul-2019.)
Assertion
Ref Expression
df-syms Syms = {𝑥(𝑥 ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}

Detailed syntax breakdown of Definition df-syms
StepHypRef Expression
1 csyms 35774 . 2 class Syms
2 vx . . . . . . 7 setvar 𝑥
32cv 1537 . . . . . 6 class 𝑥
43cdm 5523 . . . . . . 7 class dom 𝑥
53crn 5524 . . . . . . 7 class ran 𝑥
64, 5cxp 5521 . . . . . 6 class (dom 𝑥 × ran 𝑥)
73, 6cin 3882 . . . . 5 class (𝑥 ∩ (dom 𝑥 × ran 𝑥))
87ccnv 5522 . . . 4 class (𝑥 ∩ (dom 𝑥 × ran 𝑥))
9 cssr 35767 . . . 4 class S
108, 7, 9wbr 5034 . . 3 wff (𝑥 ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))
1110, 2cab 2776 . 2 class {𝑥(𝑥 ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
121, 11wceq 1538 1 wff Syms = {𝑥(𝑥 ∩ (dom 𝑥 × ran 𝑥)) S (𝑥 ∩ (dom 𝑥 × ran 𝑥))}
 Colors of variables: wff setvar class This definition is referenced by:  dfsymrels2  36092
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