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Theorem resexd 6029
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 6028 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2syl 17 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3475  cres 5679
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5300
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-in 3956  df-ss 3966  df-res 5689
This theorem is referenced by:  gsum2dlem2  19839  tsmspropd  23636  ulmss  25909  lmimdim  32720  psrbagres  41163  pwssplit4  41879  limsupresre  44460  limsupresico  44464  limsupresuz  44467  limsupres  44469  limsupresxr  44530  liminfresxr  44531  liminfresico  44535  liminfresre  44543  liminfresuz  44548
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