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Theorem sucprc 5514
 Description: A proper class is its own successor. (Contributed by NM, 3-Apr-1995.)
Assertion
Ref Expression
sucprc

Proof of Theorem sucprc
StepHypRef Expression
1 df-suc 5445 . . 3
2 snprc 4060 . . . 4
3 uneq2 3614 . . . 4
42, 3sylbi 198 . . 3
51, 4syl5eq 2475 . 2
6 un0 3787 . 2
75, 6syl6eq 2479 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wceq 1437   wcel 1868  cvv 3081   cun 3434  c0 3761  csn 3996   csuc 5441 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-v 3083  df-dif 3439  df-un 3441  df-nul 3762  df-sn 3997  df-suc 5445 This theorem is referenced by:  nsuceq0  5519  sucon  6646  ordsuc  6652  sucprcreg  8117  suc11reg  8127
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