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Definition df-bj-ind 11252
Description: Define the property of being an inductive class. (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
df-bj-ind  |-  (Ind  A  <->  (
(/)  e.  A  /\  A. x  e.  A  suc  x  e.  A )
)
Distinct variable group:    x, A

Detailed syntax breakdown of Definition df-bj-ind
StepHypRef Expression
1 cA . . 3  class  A
21wind 11251 . 2  wff Ind  A
3 c0 3275 . . . 4  class  (/)
43, 1wcel 1436 . . 3  wff  (/)  e.  A
5 vx . . . . . . 7  setvar  x
65cv 1286 . . . . . 6  class  x
76csuc 4165 . . . . 5  class  suc  x
87, 1wcel 1436 . . . 4  wff  suc  x  e.  A
98, 5, 1wral 2355 . . 3  wff  A. x  e.  A  suc  x  e.  A
104, 9wa 102 . 2  wff  ( (/)  e.  A  /\  A. x  e.  A  suc  x  e.  A )
112, 10wb 103 1  wff  (Ind  A  <->  (
(/)  e.  A  /\  A. x  e.  A  suc  x  e.  A )
)
Colors of variables: wff set class
This definition is referenced by:  bj-indsuc  11253  bj-indeq  11254  bj-bdind  11255  bj-indint  11256  bj-indind  11257  bj-dfom  11258  bj-inf2vnlem1  11295  bj-inf2vnlem2  11296
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