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Definition df-bj-ind 11291
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 11290 . 2 wff Ind 𝐴
3 c0 3275 . . . 4 class
43, 1wcel 1436 . . 3 wff ∅ ∈ 𝐴
5 vx . . . . . . 7 setvar 𝑥
65cv 1286 . . . . . 6 class 𝑥
76csuc 4168 . . . . 5 class suc 𝑥
87, 1wcel 1436 . . . 4 wff suc 𝑥𝐴
98, 5, 1wral 2355 . . 3 wff 𝑥𝐴 suc 𝑥𝐴
104, 9wa 102 . 2 wff (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴)
112, 10wb 103 1 wff (Ind 𝐴 ↔ (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴))
Colors of variables: wff set class
This definition is referenced by:  bj-indsuc  11292  bj-indeq  11293  bj-bdind  11294  bj-indint  11295  bj-indind  11296  bj-dfom  11297  bj-inf2vnlem1  11334  bj-inf2vnlem2  11335
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