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Theorem ssexd 3939
Description: A subclass of a set is a set. Deduction form of ssexg 3938. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
ssexd.1  |-  ( ph  ->  B  e.  C )
ssexd.2  |-  ( ph  ->  A  C_  B )
Assertion
Ref Expression
ssexd  |-  ( ph  ->  A  e.  _V )

Proof of Theorem ssexd
StepHypRef Expression
1 ssexd.2 . 2  |-  ( ph  ->  A  C_  B )
2 ssexd.1 . 2  |-  ( ph  ->  B  e.  C )
3 ssexg 3938 . 2  |-  ( ( A  C_  B  /\  B  e.  C )  ->  A  e.  _V )
41, 2, 3syl2anc 403 1  |-  ( ph  ->  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   _Vcvv 2610    C_ wss 2983
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-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3917
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-in 2989  df-ss 2996
This theorem is referenced by:  fex2  5111  riotaexg  5524  opabbrex  5601  f1imaen2g  6362  genipv  6797  ovshftex  9892
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