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Theorem rexv 2873
 Description: An existential quantifier restricted to the universe is unrestricted. (Contributed by NM, 26-Mar-2004.)
Assertion
Ref Expression
rexv (x V φxφ)

Proof of Theorem rexv
StepHypRef Expression
1 df-rex 2620 . 2 (x V φx(x V φ))
2 vex 2862 . . . 4 x V
32biantrur 492 . . 3 (φ ↔ (x V φ))
43exbii 1582 . 2 (xφx(x V φ))
51, 4bitr4i 243 1 (x V φxφ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wex 1541   ∈ wcel 1710  ∃wrex 2615  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-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-rex 2620  df-v 2861 This theorem is referenced by:  rexcom4  2878  spesbc  3127  df1c2  4168  elimakvg  4258  preaddccan2lem1  4454  elrn  4896  elima1c  4947  dfco2  5080  dfco2a  5081  elncs  6119  addccan2nclem1  6263
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