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Theorem 2nexaln 1631
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 1630 . . 3  |-  ( E. x E. y ph  <->  -. 
A. x A. y  -.  ph )
21bicomi 202 . 2  |-  ( -. 
A. x A. y  -.  ph  <->  E. x E. y ph )
32con1bii 331 1  |-  ( -. 
E. x E. y ph 
<-> 
A. x A. y  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   A.wal 1377   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  2mo  2382  2moOLD  2383  swrd0  12621  2spotdisj  24766  pm11.63  30907
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