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Theorem sucex 7794
Description: The successor of a set is a set. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sucex.1 𝐴 ∈ V
Assertion
Ref Expression
sucex suc 𝐴 ∈ V

Proof of Theorem sucex
StepHypRef Expression
1 sucex.1 . 2 𝐴 ∈ V
2 sucexg 7793 . 2 (𝐴 ∈ V → suc 𝐴 ∈ V)
31, 2ax-mp 5 1 suc 𝐴 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3475  suc csuc 6367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5300  ax-nul 5307  ax-pr 5428  ax-un 7725
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-sn 4630  df-pr 4632  df-uni 4910  df-suc 6371
This theorem is referenced by:  orduninsuc  7832  tfindsg  7850  tfinds2  7853  finds  7889  findsg  7890  finds2  7891  seqomlem1  8450  2oexOLD  8487  oasuc  8524  onasuc  8528  naddcllem  8675  infensuc  9155  phplem4OLD  9220  phpOLD  9222  inf0  9616  inf3lem1  9623  dfom3  9642  cantnflt  9667  cantnflem1  9684  cnfcom  9695  brttrcl2  9709  ssttrcl  9710  ttrcltr  9711  ttrclss  9715  ttrclselem2  9721  infxpenlem  10008  pwsdompw  10199  cfslb2n  10263  cfsmolem  10265  fin1a2lem12  10406  axdc4lem  10450  alephreg  10577  bnj986  33966  bnj1018g  33974  bnj1018  33975  satf  34344  dfon2lem7  34761  rdgssun  36259  dford3lem2  41766
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