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Theorem sucex 4783
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 4782 . 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 1725   _Vcvv 2948   suc csuc 4575
This theorem is referenced by:  orduninsuc  4815  tfindsg  4832  tfinds2  4835  finds  4863  findsg  4864  finds2  4865  seqomlem1  6699  oasuc  6760  onasuc  6764  infensuc  7277  phplem4  7281  php  7283  inf0  7568  inf3lem1  7575  dfom3  7594  cantnflt  7619  cantnflem1  7637  cnfcom  7649  infxpenlem  7887  pwsdompw  8076  ackbij1lem5  8096  cfslb2n  8140  cfsmolem  8142  fin1a2lem12  8283  axdc4lem  8327  alephreg  8449  dfon2lem7  25408  dford3lem2  27079  bnj986  29252  bnj1018  29260
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rex 2703  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-uni 4008  df-suc 4579
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