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Theorem sucex 6535
Description: The successor of a set is a set. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sucex.1  |-  A  e. 
_V
Assertion
Ref Expression
sucex  |-  suc  A  e.  _V

Proof of Theorem sucex
StepHypRef Expression
1 sucex.1 . 2  |-  A  e. 
_V
2 sucexg 6534 . 2  |-  ( A  e.  _V  ->  suc  A  e.  _V )
31, 2ax-mp 5 1  |-  suc  A  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758   _Vcvv 3078   suc csuc 4832
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pr 4642  ax-un 6485
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-rex 2805  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-sn 3989  df-pr 3991  df-uni 4203  df-suc 4836
This theorem is referenced by:  orduninsuc  6567  tfindsg  6584  tfinds2  6587  finds  6615  findsg  6616  finds2  6617  seqomlem1  7018  oasuc  7077  onasuc  7081  infensuc  7602  phplem4  7606  php  7608  inf0  7942  inf3lem1  7949  dfom3  7968  cantnflt  7995  cantnflem1  8012  cantnfltOLD  8025  cantnflem1OLD  8035  cnfcom  8048  cnfcomOLD  8056  infxpenlem  8295  pwsdompw  8488  ackbij1lem5  8508  cfslb2n  8552  cfsmolem  8554  fin1a2lem12  8695  axdc4lem  8739  alephreg  8861  dfon2lem7  27769  dford3lem2  29547  bnj986  32302  bnj1018  32310  bj-1ex  32799  bj-2ex  32800
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