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Theorem ssexd 4198
Description: A subclass of a set is a set. Deduction form of ssexg 4197. (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 4197 . 2  |-  ( ( A  C_  B  /\  B  e.  C )  ->  A  e.  _V )
41, 2, 3syl2anc 642 1  |-  ( ph  ->  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1701   _Vcvv 2822    C_ wss 3186
This theorem is referenced by:  mrieqv2d  13590  mrissmrcd  13591  mreexexlemd  13595  mreexexlem3d  13597  mreexexlem4d  13598  mreexexd  13599  mreexdomd  13600  acsdomd  14333  esummono  23626  opabbrex  27248  wlks  27438  trls  27448
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-v 2824  df-in 3193  df-ss 3200
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