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Theorem 2exnexn 1590
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 1589 . 2  |-  ( A. x E. y  -.  ph  <->  -. 
E. x A. y ph )
21con2bii 323 1  |-  ( E. x A. y ph  <->  -. 
A. x E. y  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177   A.wal 1549   E.wex 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178  df-ex 1551
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