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Definition df-se 4096
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 4092 . 2 wff 𝑅 Se 𝐴
4 vy . . . . . . 7 setvar 𝑦
54cv 1284 . . . . . 6 class 𝑦
6 vx . . . . . . 7 setvar 𝑥
76cv 1284 . . . . . 6 class 𝑥
85, 7, 2wbr 3793 . . . . 5 wff 𝑦𝑅𝑥
98, 4, 1crab 2353 . . . 4 class {𝑦𝐴𝑦𝑅𝑥}
10 cvv 2602 . . . 4 class V
119, 10wcel 1434 . . 3 wff {𝑦𝐴𝑦𝑅𝑥} ∈ V
1211, 6, 1wral 2349 . 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  4098  exse  4099  sess1  4100  sess2  4101  nfse  4104  epse  4105  seinxp  4437  dfse2  4728  exse2  4729
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