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Definition df-bj-ind 10438
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 10437 . 2 wff Ind 𝐴
3 c0 3252 . . . 4 class
43, 1wcel 1409 . . 3 wff ∅ ∈ 𝐴
5 vx . . . . . . 7 setvar 𝑥
65cv 1258 . . . . . 6 class 𝑥
76csuc 4130 . . . . 5 class suc 𝑥
87, 1wcel 1409 . . . 4 wff suc 𝑥𝐴
98, 5, 1wral 2323 . . 3 wff 𝑥𝐴 suc 𝑥𝐴
104, 9wa 101 . 2 wff (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴)
112, 10wb 102 1 wff (Ind 𝐴 ↔ (∅ ∈ 𝐴 ∧ ∀𝑥𝐴 suc 𝑥𝐴))
Colors of variables: wff set class
This definition is referenced by:  bj-indsuc  10439  bj-indeq  10440  bj-bdind  10441  bj-indint  10442  bj-indind  10443  bj-dfom  10444  peano5setOLD  10452  bj-inf2vnlem1  10482  bj-inf2vnlem2  10483
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