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Theorem reuv 2874
 Description: A uniqueness quantifier restricted to the universe is unrestricted. (Contributed by NM, 1-Nov-2010.)
Assertion
Ref Expression
reuv (∃!x V φ∃!xφ)

Proof of Theorem reuv
StepHypRef Expression
1 df-reu 2621 . 2 (∃!x V φ∃!x(x V φ))
2 vex 2862 . . . 4 x V
32biantrur 492 . . 3 (φ ↔ (x V φ))
43eubii 2213 . 2 (∃!xφ∃!x(x V φ))
51, 4bitr4i 243 1 (∃!x V φ∃!xφ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358   ∈ wcel 1710  ∃!weu 2204  ∃!wreu 2616  Vcvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  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-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-reu 2621  df-v 2861 This theorem is referenced by: (None)
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