Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm11.63 Unicode version

Theorem pm11.63 26993
Description: Theorem *11.63 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm11.63  |-  ( -. 
E. x E. y ph  ->  A. x A. y
( ph  ->  ps )
)

Proof of Theorem pm11.63
StepHypRef Expression
1 2nexaln 26972 . 2  |-  ( -. 
E. x E. y ph 
<-> 
A. x A. y  -.  ph )
2 pm2.21 102 . . 3  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
322alimi 1548 . 2  |-  ( A. x A. y  -.  ph  ->  A. x A. y
( ph  ->  ps )
)
41, 3sylbi 189 1  |-  ( -. 
E. x E. y ph  ->  A. x A. y
( ph  ->  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1528   E.wex 1529
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545
This theorem depends on definitions:  df-bi 179  df-ex 1530
  Copyright terms: Public domain W3C validator