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Theorem resex 4651
 Description: The restriction of a set is a set. (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
resex.1 𝐴 ∈ V
Assertion
Ref Expression
resex (𝐴𝐵) ∈ V

Proof of Theorem resex
StepHypRef Expression
1 resex.1 . 2 𝐴 ∈ V
2 resexg 4650 . 2 (𝐴 ∈ V → (𝐴𝐵) ∈ V)
31, 2ax-mp 7 1 (𝐴𝐵) ∈ V
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  Vcvv 2557   ↾ cres 4347 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-res 4357 This theorem is referenced by: (None)
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