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Theorem elsuc2g 4652
 Description: Variant of membership in a successor, requiring that rather than be a set. (Contributed by NM, 28-Oct-2003.)
Assertion
Ref Expression
elsuc2g

Proof of Theorem elsuc2g
StepHypRef Expression
1 df-suc 4590 . . 3
21eleq2i 2502 . 2
3 elun 3490 . . 3
4 elsnc2g 3844 . . . 4
54orbi2d 684 . . 3
63, 5syl5bb 250 . 2
72, 6syl5bb 250 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wo 359   wceq 1653   wcel 1726   cun 3320  csn 3816   csuc 4586 This theorem is referenced by:  elsuc2  4654  om2uzlti  11295 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-sn 3822  df-suc 4590
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