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Theorem ssexi 4066
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 4065 . 2 (𝐴𝐵𝐴 ∈ V)
41, 3ax-mp 5 1 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1480  Vcvv 2686  wss 3071
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084
This theorem is referenced by:  zfausab  4070  pp0ex  4113  ord3ex  4114  epse  4264  opabex  5644  oprabex  6026  phplem2  6747  phpm  6759  snexxph  6838  sbthlem2  6846  niex  7132  enqex  7180  enq0ex  7259  npex  7293  ltnqex  7369  gtnqex  7370  recexprlemell  7442  recexprlemelu  7443  enrex  7557  axcnex  7679  peano5nnnn  7712  reex  7766  nnex  8738  zex  9075  qex  9436  ixxex  9694  serclim0  11086  climle  11115  iserabs  11256  isumshft  11271  explecnv  11286  prodfclim1  11325  prmex  11805  exmidunben  11950  istopon  12194  dmtopon  12204  lmres  12431  climcncf  12754  reldvg  12831
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