Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  2exnaln Unicode version

Theorem 2exnaln 27583
Description: Theorem *11.22 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2exnaln  |-  ( E. x E. y ph  <->  -. 
A. x A. y  -.  ph )

Proof of Theorem 2exnaln
StepHypRef Expression
1 df-ex 1531 . 2  |-  ( E. x E. y ph  <->  -. 
A. x  -.  E. y ph )
2 alnex 1532 . . 3  |-  ( A. y  -.  ph  <->  -.  E. y ph )
32albii 1555 . 2  |-  ( A. x A. y  -.  ph  <->  A. x  -.  E. y ph )
41, 3xchbinxr 302 1  |-  ( E. x E. y ph  <->  -. 
A. x A. y  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wal 1529   E.wex 1530
This theorem is referenced by:  2nexaln  27584
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546
This theorem depends on definitions:  df-bi 177  df-ex 1531
  Copyright terms: Public domain W3C validator