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Theorem 2exnexn 1680
Description: Theorem *11.51 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.) (Proof shortened by Wolf Lammen, 25-Sep-2014.)
Assertion
Ref Expression
2exnexn  |-  ( E. x A. y ph  <->  -. 
A. x E. y  -.  ph )

Proof of Theorem 2exnexn
StepHypRef Expression
1 alexn 1679 . 2  |-  ( A. x E. y  -.  ph  <->  -. 
E. x A. y ph )
21con2bii 330 1  |-  ( E. x A. y ph  <->  -. 
A. x E. y  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   A.wal 1397   E.wex 1627
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1633  ax-4 1646
This theorem depends on definitions:  df-bi 185  df-ex 1628
This theorem is referenced by: (None)
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