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Definition df-se 4160
Description: Define the set-like predicate. (Contributed by Mario Carneiro, 19-Nov-2014.)
Assertion
Ref Expression
df-se (𝑅 Se 𝐴 ↔ ∀𝑥𝐴 {𝑦𝐴𝑦𝑅𝑥} ∈ V)
Distinct variable groups:   𝑥,𝑦,𝑅   𝑥,𝐴,𝑦

Detailed syntax breakdown of Definition df-se
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cR . . 3 class 𝑅
31, 2wse 4156 . 2 wff 𝑅 Se 𝐴
4 vy . . . . . . 7 setvar 𝑦
54cv 1288 . . . . . 6 class 𝑦
6 vx . . . . . . 7 setvar 𝑥
76cv 1288 . . . . . 6 class 𝑥
85, 7, 2wbr 3845 . . . . 5 wff 𝑦𝑅𝑥
98, 4, 1crab 2363 . . . 4 class {𝑦𝐴𝑦𝑅𝑥}
10 cvv 2619 . . . 4 class V
119, 10wcel 1438 . . 3 wff {𝑦𝐴𝑦𝑅𝑥} ∈ V
1211, 6, 1wral 2359 . 2 wff 𝑥𝐴 {𝑦𝐴𝑦𝑅𝑥} ∈ V
133, 12wb 103 1 wff (𝑅 Se 𝐴 ↔ ∀𝑥𝐴 {𝑦𝐴𝑦𝑅𝑥} ∈ V)
Colors of variables: wff set class
This definition is referenced by:  seex  4162  exse  4163  sess1  4164  sess2  4165  nfse  4168  epse  4169  seinxp  4509  dfse2  4805  exse2  4806
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