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Theorem sucex 4826
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 4825 . 2  |-  ( A  e.  _V  ->  suc  A  e.  _V )
31, 2ax-mp 5 1  |-  suc  A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1728   _Vcvv 2965   suc csuc 4618
This theorem is referenced by:  orduninsuc  4858  tfindsg  4875  tfinds2  4878  finds  4906  findsg  4907  finds2  4908  seqomlem1  6743  oasuc  6804  onasuc  6808  infensuc  7321  phplem4  7325  php  7327  inf0  7612  inf3lem1  7619  dfom3  7638  cantnflt  7663  cantnflem1  7681  cnfcom  7693  infxpenlem  7933  pwsdompw  8122  ackbij1lem5  8142  cfslb2n  8186  cfsmolem  8188  fin1a2lem12  8329  axdc4lem  8373  alephreg  8495  dfon2lem7  25451  dford3lem2  27210  bnj986  29499  bnj1018  29507
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-13 1730  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4361  ax-nul 4369  ax-pr 4438  ax-un 4736
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-rex 2718  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-sn 3849  df-pr 3850  df-uni 4045  df-suc 4622
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