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Theorem resex 4864
 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 4863 . 2 (𝐴 ∈ V → (𝐴𝐵) ∈ V)
31, 2ax-mp 5 1 (𝐴𝐵) ∈ V
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1481  Vcvv 2687   ↾ cres 4545 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4050 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2689  df-in 3078  df-ss 3085  df-res 4555 This theorem is referenced by:  sbthlemi10  6858  finomni  7016  ctinf  11970
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