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Definition df-bj-ind 10907
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 10906 . 2  wff Ind  A
3 c0 3258 . . . 4  class  (/)
43, 1wcel 1434 . . 3  wff  (/)  e.  A
5 vx . . . . . . 7  setvar  x
65cv 1284 . . . . . 6  class  x
76csuc 4128 . . . . 5  class  suc  x
87, 1wcel 1434 . . . 4  wff  suc  x  e.  A
98, 5, 1wral 2349 . . 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  10908  bj-indeq  10909  bj-bdind  10910  bj-indint  10911  bj-indind  10912  bj-dfom  10913  bj-inf2vnlem1  10950  bj-inf2vnlem2  10951
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