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Theorem sucex 7791
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 7790 . 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 6364
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 5299  ax-nul 5306  ax-pr 5427  ax-un 7722
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 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-sn 4629  df-pr 4631  df-uni 4909  df-suc 6368
This theorem is referenced by:  orduninsuc  7829  tfindsg  7847  tfinds2  7850  finds  7886  findsg  7887  finds2  7888  seqomlem1  8447  2oexOLD  8484  oasuc  8521  onasuc  8525  naddcllem  8672  infensuc  9152  phplem4OLD  9217  phpOLD  9219  inf0  9613  inf3lem1  9620  dfom3  9639  cantnflt  9664  cantnflem1  9681  cnfcom  9692  brttrcl2  9706  ssttrcl  9707  ttrcltr  9708  ttrclss  9712  ttrclselem2  9718  infxpenlem  10005  pwsdompw  10196  cfslb2n  10260  cfsmolem  10262  fin1a2lem12  10403  axdc4lem  10447  alephreg  10574  bnj986  33955  bnj1018g  33963  bnj1018  33964  satf  34333  dfon2lem7  34750  rdgssun  36248  dford3lem2  41752
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