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Theorem ssexi 4138
Description: The subset of a set is also a set. (Contributed by NM, 9-Sep-1993.)
Hypotheses
Ref Expression
ssexi.1  |-  B  e. 
_V
ssexi.2  |-  A  C_  B
Assertion
Ref Expression
ssexi  |-  A  e. 
_V

Proof of Theorem ssexi
StepHypRef Expression
1 ssexi.2 . 2  |-  A  C_  B
2 ssexi.1 . . 3  |-  B  e. 
_V
32ssex 4137 . 2  |-  ( A 
C_  B  ->  A  e.  _V )
41, 3ax-mp 5 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 2148   _Vcvv 2737    C_ wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-sep 4118
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-in 3135  df-ss 3142
This theorem is referenced by:  zfausab  4142  pp0ex  4186  ord3ex  4187  epse  4339  opabex  5736  mptexw  6108  oprabex  6123  mpoexw  6208  phplem2  6847  phpm  6859  snexxph  6943  sbthlem2  6951  2omotaplemst  7247  niex  7299  enqex  7347  enq0ex  7426  npex  7460  ltnqex  7536  gtnqex  7537  recexprlemell  7609  recexprlemelu  7610  enrex  7724  axcnex  7846  peano5nnnn  7879  reex  7933  nnex  8911  zex  9248  qex  9618  ixxex  9883  iccen  9990  serclim0  11294  climle  11323  iserabs  11464  isumshft  11479  explecnv  11494  prodfclim1  11533  prmex  12093  exmidunben  12407  istopon  13171  dmtopon  13181  lmres  13408  climcncf  13731  reldvg  13808
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