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Theorem ralv 2698
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 2419 . 2  |-  ( A. x  e.  _V  ph  <->  A. x
( x  e.  _V  ->  ph ) )
2 vex 2684 . . . 4  |-  x  e. 
_V
32a1bi 242 . . 3  |-  ( ph  <->  ( x  e.  _V  ->  ph ) )
43albii 1446 . 2  |-  ( A. x ph  <->  A. x ( x  e.  _V  ->  ph )
)
51, 4bitr4i 186 1  |-  ( A. x  e.  _V  ph  <->  A. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1329    e. wcel 1480   A.wral 2414   _Vcvv 2681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-ral 2419  df-v 2683
This theorem is referenced by:  ralcom4  2703  viin  3867  issref  4916  frecrdg  6298
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