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Theorem dfral2 2869
Description: Relationship between restricted universal and existential quantifiers. (Contributed by NM, 21-Jan-1997.)
Assertion
Ref Expression
dfral2  |-  ( A. x  e.  A  ph  <->  -.  E. x  e.  A  -.  ph )

Proof of Theorem dfral2
StepHypRef Expression
1 rexnal 2842 . 2  |-  ( E. x  e.  A  -.  ph  <->  -. 
A. x  e.  A  ph )
21con2bii 332 1  |-  ( A. x  e.  A  ph  <->  -.  E. x  e.  A  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   A.wral 2795   E.wrex 2796
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-ral 2800  df-rex 2801
This theorem is referenced by:  boxcutc  7408  infssuni  7705  ac6n  8757  indstr  11026  trfil3  19579  tglowdim2ln  23181  nmobndseqi  24316  stri  25798  hstri  25806  bnj1204  32305
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