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Theorem elsuc2g 4952
 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 4890 . . 3
21eleq2i 2545 . 2
3 elun 3650 . . 3
4 elsnc2g 4063 . . . 4
54orbi2d 701 . . 3
63, 5syl5bb 257 . 2
72, 6syl5bb 257 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wo 368   wceq 1379   wcel 1767   cun 3479  csn 4033   csuc 4886 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3120  df-un 3486  df-sn 4034  df-suc 4890 This theorem is referenced by:  elsuc2  4954  om2uzlti  12041
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