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Theorem elsuc2g 4168
 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 4134 . . 3
21eleq2i 2146 . 2
3 elun 3114 . . 3
4 elsn2g 3435 . . . 4
54orbi2d 737 . . 3
63, 5syl5bb 190 . 2
72, 6syl5bb 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wo 662   wceq 1285   wcel 1434   cun 2972  csn 3406   csuc 4128 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-sn 3412  df-suc 4134 This theorem is referenced by:  elsuc2  4170  nntri3or  6137  frec2uzltd  9485
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