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Theorem sucidg 4347
 Description: Part of Proposition 7.23 of [TakeutiZaring] p. 41 (generalized). (Contributed by NM, 25-Mar-1995.) (Proof shortened by Scott Fenton, 20-Feb-2012.)
Assertion
Ref Expression
sucidg

Proof of Theorem sucidg
StepHypRef Expression
1 eqid 2140 . . 3
21olci 722 . 2
3 elsucg 4335 . 2
42, 3mpbiri 167 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 698   wceq 1332   wcel 1481   csuc 4296 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-sn 3539  df-suc 4302 This theorem is referenced by:  sucid  4348  nsuceq0g  4349  trsuc  4353  sucssel  4355  ordsucg  4427  sucunielr  4435  suc11g  4481  nlimsucg  4490  peano2b  4537  omsinds  4544  frecsuclem  6312  phplem4dom  6765  phplem4on  6770  dif1en  6782  fin0  6788  fin0or  6789  fidcenumlemrks  6851  bj-peano4  13344
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