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Theorem dfral2 2568
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 2567 . 2  |-  ( E. x  e.  A  -.  ph  <->  -. 
A. x  e.  A  ph )
21con2bii 322 1  |-  ( A. x  e.  A  ph  <->  -.  E. x  e.  A  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wral 2556   E.wrex 2557
This theorem is referenced by:  boxcutc  6875  ac6n  8128  indstr  10303  trfil3  17599  nmobndseqi  21373  stri  22853  hstri  22861  isunscov  25177  bnj1204  29358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-ral 2561  df-rex 2562
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