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Theorem 2nalexn 1565
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 1534 . . 3  |-  ( E. x E. y  -. 
ph 
<->  -.  A. x  -.  E. y  -.  ph )
2 alex 1564 . . . 4  |-  ( A. y ph  <->  -.  E. y  -.  ph )
32albii 1558 . . 3  |-  ( A. x A. y ph  <->  A. x  -.  E. y  -.  ph )
41, 3xchbinxr 304 . 2  |-  ( E. x E. y  -. 
ph 
<->  -.  A. x A. y ph )
54bicomi 195 1  |-  ( -. 
A. x A. y ph 
<->  E. x E. y  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178   A.wal 1532   E.wex 1533
This theorem is referenced by:  spc2gv  2872  hashfun  11383  pm11.52  26984  2exanali  26985
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549
This theorem depends on definitions:  df-bi 179  df-ex 1534
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