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Theorem dfral2 2709
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 2708 . 2  |-  ( E. x  e.  A  -.  ph  <->  -. 
A. x  e.  A  ph )
21con2bii 323 1  |-  ( A. x  e.  A  ph  <->  -.  E. x  e.  A  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177   A.wral 2697   E.wrex 2698
This theorem is referenced by:  boxcutc  7097  infssuni  7389  ac6n  8357  indstr  10537  trfil3  17912  nmobndseqi  22272  stri  23752  hstri  23760  bnj1204  29318
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-ral 2702  df-rex 2703
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