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Definition df-bj-ind 7150
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 7149 . 2 wff Ind A
3 c0 3201 . . . 4 class
43, 1wcel 1374 . . 3 wff A
5 vx . . . . . . 7 setvar x
65cv 1227 . . . . . 6 class x
76csuc 4051 . . . . 5 class suc x
87, 1wcel 1374 . . . 4 wff suc x A
98, 5, 1wral 2284 . . 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  7151  bj-indeq  7152  bj-bdind  7153  bj-indint  7154  bj-dfom  7155  bj-inf2vnlem1  7188  bj-inf2vnlem2  7189
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