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

Theorem bj-indeq 10053
 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 10051 . 2 Ind
2 df-bj-ind 10051 . . 3 Ind
3 eleq2 2101 . . . . 5
43bicomd 129 . . . 4
5 eleq2 2101 . . . . . 6
65raleqbi1dv 2513 . . . . 5
76bicomd 129 . . . 4
84, 7anbi12d 442 . . 3
92, 8syl5rbb 182 . 2 Ind
101, 9syl5bb 181 1 Ind Ind
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243   wcel 1393  wral 2306  c0 3224   csuc 4102  Ind wind 10050 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-bj-ind 10051 This theorem is referenced by:  bj-omind  10058  bj-omssind  10059  bj-ssom  10060  bj-om  10061  bj-2inf  10062  peano5setOLD  10065
 Copyright terms: Public domain W3C validator