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Definition df-bnj13 29816
Description: Define the following predicate: 𝑅 is set-like on 𝐴. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
df-bnj13 (𝑅 Se 𝐴 ↔ ∀𝑥𝐴 pred(𝑥, 𝐴, 𝑅) ∈ V)
Distinct variable groups:   𝑥,𝑅   𝑥,𝐴

Detailed syntax breakdown of Definition df-bnj13
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cR . . 3 class 𝑅
31, 2w-bnj13 29815 . 2 wff 𝑅 Se 𝐴
4 vx . . . . . 6 setvar 𝑥
54cv 1473 . . . . 5 class 𝑥
61, 2, 5c-bnj14 29813 . . . 4 class pred(𝑥, 𝐴, 𝑅)
7 cvv 3172 . . . 4 class V
86, 7wcel 1976 . . 3 wff pred(𝑥, 𝐴, 𝑅) ∈ V
98, 4, 1wral 2895 . 2 wff 𝑥𝐴 pred(𝑥, 𝐴, 𝑅) ∈ V
103, 9wb 194 1 wff (𝑅 Se 𝐴 ↔ ∀𝑥𝐴 pred(𝑥, 𝐴, 𝑅) ∈ V)
Colors of variables: wff setvar class
This definition is referenced by:  bnj93  29993  bnj1489  30184
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