Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  df-bj-ind Unicode version

Definition df-bj-ind 13962
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 13961 . 2  wff Ind  A
3 c0 3414 . . . 4  class  (/)
43, 1wcel 2141 . . 3  wff  (/)  e.  A
5 vx . . . . . . 7  setvar  x
65cv 1347 . . . . . 6  class  x
76csuc 4350 . . . . 5  class  suc  x
87, 1wcel 2141 . . . 4  wff  suc  x  e.  A
98, 5, 1wral 2448 . . 3  wff  A. x  e.  A  suc  x  e.  A
104, 9wa 103 . 2  wff  ( (/)  e.  A  /\  A. x  e.  A  suc  x  e.  A )
112, 10wb 104 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  13963  bj-indeq  13964  bj-bdind  13965  bj-indint  13966  bj-indind  13967  bj-dfom  13968  bj-inf2vnlem1  14005  bj-inf2vnlem2  14006
  Copyright terms: Public domain W3C validator