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Theorem ralv 2814
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 2561 . 2  |-  ( A. x  e.  _V  ph  <->  A. x
( x  e.  _V  ->  ph ) )
2 vex 2804 . . . 4  |-  x  e. 
_V
32a1bi 327 . . 3  |-  ( ph  <->  ( x  e.  _V  ->  ph ) )
43albii 1556 . 2  |-  ( A. x ph  <->  A. x ( x  e.  _V  ->  ph )
)
51, 4bitr4i 243 1  |-  ( A. x  e.  _V  ph  <->  A. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530    e. wcel 1696   A.wral 2556   _Vcvv 2801
This theorem is referenced by:  ralcom4  2819  viin  3977  issref  5072  ralcom4f  23149  hfext  24885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-ral 2561  df-v 2803
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