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Theorem rabab 2569
Description: A class abstraction restricted to the universe is unrestricted. (Contributed by NM, 27-Dec-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
rabab {x V ∣ φ} = {xφ}

Proof of Theorem rabab
StepHypRef Expression
1 df-rab 2309 . 2 {x V ∣ φ} = {x ∣ (x V φ)}
2 vex 2554 . . . 4 x V
32biantrur 287 . . 3 (φ ↔ (x V φ))
43abbii 2150 . 2 {xφ} = {x ∣ (x V φ)}
51, 4eqtr4i 2060 1 {x V ∣ φ} = {xφ}
Colors of variables: wff set class
Syntax hints:   wa 97   = wceq 1242   wcel 1390  {cab 2023  {crab 2304  Vcvv 2551
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-rab 2309  df-v 2553
This theorem is referenced by:  notab  3201  intmin2  3632  euen1  6218  bj-omind  9322
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