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Theorem 2nexaln 27573
Description: Theorem *11.25 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2nexaln  |-  ( -. 
E. x E. y ph 
<-> 
A. x A. y  -.  ph )

Proof of Theorem 2nexaln
StepHypRef Expression
1 2exnaln 27572 . . 3  |-  ( E. x E. y ph  <->  -. 
A. x A. y  -.  ph )
21bicomi 193 . 2  |-  ( -. 
A. x A. y  -.  ph  <->  E. x E. y ph )
32con1bii 321 1  |-  ( -. 
E. x E. y ph 
<-> 
A. x A. y  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wal 1527   E.wex 1528
This theorem is referenced by:  pm11.63  27594
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-ex 1529
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