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Theorem ralv 3092
Description: A universal quantifier restricted to the universe is unrestricted. (Contributed by NM, 26-Mar-2004.)
Assertion
Ref Expression
ralv  |-  ( A. x  e.  _V  ph  <->  A. x ph )

Proof of Theorem ralv
StepHypRef Expression
1 df-ral 2804 . 2  |-  ( A. x  e.  _V  ph  <->  A. x
( x  e.  _V  ->  ph ) )
2 vex 3081 . . . 4  |-  x  e. 
_V
32a1bi 337 . . 3  |-  ( ph  <->  ( x  e.  _V  ->  ph ) )
43albii 1611 . 2  |-  ( A. x ph  <->  A. x ( x  e.  _V  ->  ph )
)
51, 4bitr4i 252 1  |-  ( A. x  e.  _V  ph  <->  A. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1368    e. wcel 1758   A.wral 2799   _Vcvv 3078
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-ral 2804  df-v 3080
This theorem is referenced by:  ralcom4  3097  viin  4340  issref  5322  ralcom4f  26039  hfext  28388
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