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Theorem 2exnaln 27572
Description: Theorem *11.22 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2exnaln  |-  ( E. x E. y ph  <->  -. 
A. x A. y  -.  ph )

Proof of Theorem 2exnaln
StepHypRef Expression
1 df-ex 1529 . 2  |-  ( E. x E. y ph  <->  -. 
A. x  -.  E. y ph )
2 alnex 1530 . . 3  |-  ( A. y  -.  ph  <->  -.  E. y ph )
32albii 1553 . 2  |-  ( A. x A. y  -.  ph  <->  A. x  -.  E. y ph )
41, 3xchbinxr 302 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:  2nexaln  27573
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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