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Theorem 2nalexn 1563
Description: Part of theorem *11.5 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2nalexn  |-  ( -. 
A. x A. y ph 
<->  E. x E. y  -.  ph )

Proof of Theorem 2nalexn
StepHypRef Expression
1 df-ex 1532 . . 3  |-  ( E. x E. y  -. 
ph 
<->  -.  A. x  -.  E. y  -.  ph )
2 alex 1562 . . . 4  |-  ( A. y ph  <->  -.  E. y  -.  ph )
32albii 1556 . . 3  |-  ( A. x A. y ph  <->  A. x  -.  E. y  -.  ph )
41, 3xchbinxr 302 . 2  |-  ( E. x E. y  -. 
ph 
<->  -.  A. x A. y ph )
54bicomi 193 1  |-  ( -. 
A. x A. y ph 
<->  E. x E. y  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wal 1530   E.wex 1531
This theorem is referenced by:  spc2gv  2884  hashfun  11405  pm11.52  27688  2exanali  27689
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-ex 1532
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