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Theorem resexd 5982
Description: The restriction of a set is a set. (Contributed by Glauco Siliprandi, 23-Oct-2021.)
Hypothesis
Ref Expression
resexd.1 (𝜑𝐴𝑉)
Assertion
Ref Expression
resexd (𝜑 → (𝐴𝐵) ∈ V)

Proof of Theorem resexd
StepHypRef Expression
1 resexd.1 . 2 (𝜑𝐴𝑉)
2 resexg 5981 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2syl 17 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Vcvv 3443  cres 5633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-sep 5254
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3406  df-v 3445  df-in 3915  df-ss 3925  df-res 5643
This theorem is referenced by:  gsum2dlem2  19739  tsmspropd  23467  ulmss  25740  pwssplit4  41354  limsupresre  43869  limsupresico  43873  limsupresuz  43876  limsupres  43878  limsupresxr  43939  liminfresxr  43940  liminfresico  43944  liminfresre  43952  liminfresuz  43957
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