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Theorem pm11.63 27697
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 27676 . 2  |-  ( -. 
E. x E. y ph 
<-> 
A. x A. y  -.  ph )
2 pm2.21 100 . . 3  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
322alimi 1550 . 2  |-  ( A. x A. y  -.  ph  ->  A. x A. y
( ph  ->  ps )
)
41, 3sylbi 187 1  |-  ( -. 
E. x E. y ph  ->  A. x A. y
( ph  ->  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530   E.wex 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-ex 1532
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