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Theorem bj-indeq 13271
 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 13269 . 2 Ind
2 df-bj-ind 13269 . . 3 Ind
3 eleq2 2203 . . . . 5
43bicomd 140 . . . 4
5 eleq2 2203 . . . . . 6
65raleqbi1dv 2634 . . . . 5
76bicomd 140 . . . 4
84, 7anbi12d 464 . . 3
92, 8syl5rbb 192 . 2 Ind
101, 9syl5bb 191 1 Ind Ind
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331   wcel 1480  wral 2416  c0 3363   csuc 4290  Ind wind 13268 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-bj-ind 13269 This theorem is referenced by:  bj-omind  13276  bj-omssind  13277  bj-ssom  13278  bj-om  13279  bj-2inf  13280
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