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Theorem elsuc 4337
 Description: Membership in a successor. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 15-Sep-2003.)
Hypothesis
Ref Expression
elsuc.1
Assertion
Ref Expression
elsuc

Proof of Theorem elsuc
StepHypRef Expression
1 elsuc.1 . 2
2 elsucg 4335 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wb 104   wo 698   wceq 1332   wcel 1481  cvv 2690   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:  sucel  4341  suctr  4352  0elsucexmid  4489  tfrlemisucaccv  6231  tfr1onlemsucaccv  6247  tfrcllemsucaccv  6260
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