Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  df-bj-ind GIF version

Definition df-bj-ind 12088
 Description: Define the property of being an inductive class. (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
df-bj-ind (Ind 𝐴 ↔ (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴))
Distinct variable group:   𝑥,𝐴

Detailed syntax breakdown of Definition df-bj-ind
StepHypRef Expression
1 cA . . 3 class 𝐴
21wind 12087 . 2 wff Ind 𝐴
3 c0 3287 . . . 4 class
43, 1wcel 1439 . . 3 wff ∅ ∈ 𝐴
5 vx . . . . . . 7 setvar 𝑥
65cv 1289 . . . . . 6 class 𝑥
76csuc 4201 . . . . 5 class suc 𝑥
87, 1wcel 1439 . . . 4 wff suc 𝑥𝐴
98, 5, 1wral 2360 . . 3 wff 𝑥𝐴 suc 𝑥𝐴
104, 9wa 103 . 2 wff (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴)
112, 10wb 104 1 wff (Ind 𝐴 ↔ (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴))
 Colors of variables: wff set class This definition is referenced by:  bj-indsuc  12089  bj-indeq  12090  bj-bdind  12091  bj-indint  12092  bj-indind  12093  bj-dfom  12094  bj-inf2vnlem1  12131  bj-inf2vnlem2  12132
 Copyright terms: Public domain W3C validator