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Theorem sucexg 4250
Description: The successor of a set is a set (generalization). (Contributed by NM, 5-Jun-1994.)
Assertion
Ref Expression
sucexg  |-  ( A  e.  V  ->  suc  A  e.  _V )

Proof of Theorem sucexg
StepHypRef Expression
1 elex 2611 . 2  |-  ( A  e.  V  ->  A  e.  _V )
2 sucexb 4249 . 2  |-  ( A  e.  _V  <->  suc  A  e. 
_V )
31, 2sylib 120 1  |-  ( A  e.  V  ->  suc  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   _Vcvv 2602   suc csuc 4128
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972  ax-un 4196
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-uni 3610  df-suc 4134
This theorem is referenced by:  sucex  4251  suceloni  4253  peano2  4344  sucinc2  6090  oav2  6107
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