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Theorem sucex 7746
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 7745 . 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 3448  suc csuc 6324
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 2708  ax-sep 5261  ax-nul 5268  ax-pr 5389  ax-un 7677
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 2715  df-cleq 2729  df-clel 2815  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-sn 4592  df-pr 4594  df-uni 4871  df-suc 6328
This theorem is referenced by:  orduninsuc  7784  tfindsg  7802  tfinds2  7805  finds  7840  findsg  7841  finds2  7842  seqomlem1  8401  2oexOLD  8438  oasuc  8475  onasuc  8479  naddcllem  8627  infensuc  9106  phplem4OLD  9171  phpOLD  9173  inf0  9564  inf3lem1  9571  dfom3  9590  cantnflt  9615  cantnflem1  9632  cnfcom  9643  brttrcl2  9657  ssttrcl  9658  ttrcltr  9659  ttrclss  9663  ttrclselem2  9669  infxpenlem  9956  pwsdompw  10147  cfslb2n  10211  cfsmolem  10213  fin1a2lem12  10354  axdc4lem  10398  alephreg  10525  bnj986  33607  bnj1018g  33615  bnj1018  33616  satf  33987  dfon2lem7  34403  rdgssun  35878  dford3lem2  41380
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