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Theorem 2exanali 26939
Description: Theorem *11.521 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2exanali  |-  ( -. 
E. x E. y
( ph  /\  -.  ps ) 
<-> 
A. x A. y
( ph  ->  ps )
)

Proof of Theorem 2exanali
StepHypRef Expression
1 2nalexn 1571 . . 3  |-  ( -. 
A. x A. y
( ph  ->  ps )  <->  E. x E. y  -.  ( ph  ->  ps ) )
21con1bii 323 . 2  |-  ( -. 
E. x E. y  -.  ( ph  ->  ps ) 
<-> 
A. x A. y
( ph  ->  ps )
)
3 annim 416 . . 3  |-  ( (
ph  /\  -.  ps )  <->  -.  ( ph  ->  ps ) )
432exbii 1581 . 2  |-  ( E. x E. y (
ph  /\  -.  ps )  <->  E. x E. y  -.  ( ph  ->  ps ) )
52, 4xchnxbir 302 1  |-  ( -. 
E. x E. y
( ph  /\  -.  ps ) 
<-> 
A. x A. y
( ph  ->  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178    /\ wa 360   A.wal 1532   E.wex 1537
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538
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