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Theorem resexd 39635
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 5477 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2syl 17 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2030  Vcvv 3231  cres 5145
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-in 3614  df-ss 3621  df-res 5155
This theorem is referenced by:  limsupresre  40246  limsupresico  40250  limsupresuz  40253  limsupres  40255  limsupresxr  40316  liminfresxr  40317  liminfresico  40321  liminfresre  40329  liminfresuz  40334
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