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Theorem rabab 2876
 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} = {x φ}

Proof of Theorem rabab
StepHypRef Expression
1 df-rab 2623 . 2 {x V φ} = {x (x V φ)}
2 vex 2862 . . . 4 x V
32biantrur 492 . . 3 (φ ↔ (x V φ))
43abbii 2465 . 2 {x φ} = {x (x V φ)}
51, 4eqtr4i 2376 1 {x V φ} = {x φ}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  {cab 2339  {crab 2618  Vcvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-rab 2623  df-v 2861 This theorem is referenced by:  notab  3525  intmin2  3953
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