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Theorem bj-indsuc 10052
 Description: A direct consequence of the definition of Ind. (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
bj-indsuc Ind

Proof of Theorem bj-indsuc
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-bj-ind 10051 . . 3 Ind
21simprbi 260 . 2 Ind
3 suceq 4139 . . . 4
43eleq1d 2106 . . 3
54rspcv 2652 . 2
62, 5syl5com 26 1 Ind
 Colors of variables: wff set class Syntax hints:   wi 4   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-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-un 2922  df-sn 3381  df-suc 4108  df-bj-ind 10051 This theorem is referenced by:  bj-indint  10055  bj-peano2  10063  bj-inf2vnlem2  10096
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