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

Theorem bj-indeq 9388
Description: Equality property for Ind. (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
bj-indeq Ind Ind

Proof of Theorem bj-indeq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-bj-ind 9386 . 2 Ind  (/)  suc
2 df-bj-ind 9386 . . 3 Ind  (/)  suc
3 eleq2 2098 . . . . 5  (/)  (/)
43bicomd 129 . . . 4  (/)  (/)
5 eleq2 2098 . . . . . 6  suc  suc
65raleqbi1dv 2507 . . . . 5  suc  suc
76bicomd 129 . . . 4  suc  suc
84, 7anbi12d 442 . . 3  (/)  suc  (/)  suc
92, 8syl5rbb 182 . 2  (/)  suc Ind
101, 9syl5bb 181 1 Ind Ind
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   wcel 1390  wral 2300   (/)c0 3218   suc csuc 4068  Ind wind 9385
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-bj-ind 9386
This theorem is referenced by:  bj-omind  9393  bj-omssind  9394  bj-ssom  9395  bj-om  9396  bj-2inf  9397  peano5setOLD  9400
  Copyright terms: Public domain W3C validator