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Theorem sucex 4602
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 4601 . 2  |-  ( A  e.  _V  ->  suc  A  e.  _V )
31, 2ax-mp 8 1  |-  suc  A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   _Vcvv 2788   suc csuc 4394
This theorem is referenced by:  orduninsuc  4634  tfindsg  4651  tfinds2  4654  finds  4682  findsg  4683  finds2  4684  seqomlem1  6462  oasuc  6523  onasuc  6527  infensuc  7039  phplem4  7043  php  7045  inf0  7322  inf3lem1  7329  dfom3  7348  cantnflt  7373  cantnflem1  7391  cnfcom  7403  infxpenlem  7641  pwsdompw  7830  ackbij1lem5  7850  cfslb2n  7894  cfsmolem  7896  fin1a2lem12  8037  axdc4lem  8081  alephreg  8204  dfon2lem7  23556  dford3lem2  26532  bnj986  28359  bnj1018  28367
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rex 2549  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-pr 3647  df-uni 3828  df-suc 4398
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