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Definition df-bj-ind 10051
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 10050 . 2 wff Ind 𝐴
3 c0 3224 . . . 4 class
43, 1wcel 1393 . . 3 wff ∅ ∈ 𝐴
5 vx . . . . . . 7 setvar 𝑥
65cv 1242 . . . . . 6 class 𝑥
76csuc 4102 . . . . 5 class suc 𝑥
87, 1wcel 1393 . . . 4 wff suc 𝑥𝐴
98, 5, 1wral 2306 . . 3 wff 𝑥𝐴 suc 𝑥𝐴
104, 9wa 97 . 2 wff (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴)
112, 10wb 98 1 wff (Ind 𝐴 ↔ (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴))
Colors of variables: wff set class
This definition is referenced by:  bj-indsuc  10052  bj-indeq  10053  bj-bdind  10054  bj-indint  10055  bj-indind  10056  bj-dfom  10057  peano5setOLD  10065  bj-inf2vnlem1  10095  bj-inf2vnlem2  10096
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