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Definition df-bj-ind 9316
Description: Define the property of being an inductive class. (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
df-bj-ind (Ind A ↔ (∅ A x A suc x A))
Distinct variable group:   x,A

Detailed syntax breakdown of Definition df-bj-ind
StepHypRef Expression
1 cA . . 3 class A
21wind 9315 . 2 wff Ind A
3 c0 3218 . . . 4 class
43, 1wcel 1390 . . 3 wff A
5 vx . . . . . . 7 setvar x
65cv 1241 . . . . . 6 class x
76csuc 4068 . . . . 5 class suc x
87, 1wcel 1390 . . . 4 wff suc x A
98, 5, 1wral 2300 . . 3 wff x A suc x A
104, 9wa 97 . 2 wff (∅ A x A suc x A)
112, 10wb 98 1 wff (Ind A ↔ (∅ A x A suc x A))
Colors of variables: wff set class
This definition is referenced by:  bj-indsuc  9317  bj-indeq  9318  bj-bdind  9319  bj-indint  9320  bj-dfom  9321  bj-inf2vnlem1  9354  bj-inf2vnlem2  9355
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