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Theorem ssexd 3971
Description: A subclass of a set is a set. Deduction form of ssexg 3970. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
ssexd.1 (𝜑𝐵𝐶)
ssexd.2 (𝜑𝐴𝐵)
Assertion
Ref Expression
ssexd (𝜑𝐴 ∈ V)

Proof of Theorem ssexd
StepHypRef Expression
1 ssexd.2 . 2 (𝜑𝐴𝐵)
2 ssexd.1 . 2 (𝜑𝐵𝐶)
3 ssexg 3970 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
41, 2, 3syl2anc 403 1 (𝜑𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1438  Vcvv 2619  wss 2997
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-in 3003  df-ss 3010
This theorem is referenced by:  fex2  5164  riotaexg  5594  opabbrex  5675  f1imaen2g  6490  genipv  7047  hashfacen  10206  ovshftex  10218
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