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Theorem ssexi 4006
Description: The subset of a set is also a set. (Contributed by NM, 9-Sep-1993.)
Hypotheses
Ref Expression
ssexi.1 𝐵 ∈ V
ssexi.2 𝐴𝐵
Assertion
Ref Expression
ssexi 𝐴 ∈ V

Proof of Theorem ssexi
StepHypRef Expression
1 ssexi.2 . 2 𝐴𝐵
2 ssexi.1 . . 3 𝐵 ∈ V
32ssex 4005 . 2 (𝐴𝐵𝐴 ∈ V)
41, 3ax-mp 7 1 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1448  Vcvv 2641  wss 3021
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-in 3027  df-ss 3034
This theorem is referenced by:  zfausab  4010  pp0ex  4053  ord3ex  4054  epse  4202  opabex  5576  oprabex  5957  phplem2  6676  phpm  6688  snexxph  6766  sbthlem2  6774  niex  7021  enqex  7069  enq0ex  7148  npex  7182  ltnqex  7258  gtnqex  7259  recexprlemell  7331  recexprlemelu  7332  enrex  7433  axcnex  7546  peano5nnnn  7577  reex  7626  nnex  8584  zex  8915  qex  9274  ixxex  9523  serclim0  10913  climle  10942  iserabs  11083  isumshft  11098  explecnv  11113  prmex  11587  exmidunben  11731  istopon  11962  dmtopon  11972  lmres  12198  climcncf  12484  reldvg  12521
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