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Theorem elsucg 4640
 Description: Membership in a successor. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 15-Sep-1995.)
Assertion
Ref Expression
elsucg

Proof of Theorem elsucg
StepHypRef Expression
1 df-suc 4579 . . . 4
21eleq2i 2499 . . 3
3 elun 3480 . . 3
42, 3bitri 241 . 2
5 elsncg 3828 . . 3
65orbi2d 683 . 2
74, 6syl5bb 249 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wo 358   wceq 1652   wcel 1725   cun 3310  csn 3806   csuc 4575 This theorem is referenced by:  elsuc  4642  elelsuc  4645  sucidg  4651  ordsssuc  4660  ordsucelsuc  4794  suc11reg  7566  nlt1pi  8775 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-sn 3812  df-suc 4579
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