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Theorem pm11.63 36739
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 1701 . 2  |-  ( -. 
E. x E. y ph 
<-> 
A. x A. y  -.  ph )
2 pm2.21 112 . . 3  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
322alimi 1684 . 2  |-  ( A. x A. y  -.  ph  ->  A. x A. y
( ph  ->  ps )
)
41, 3sylbi 199 1  |-  ( -. 
E. x E. y ph  ->  A. x A. y
( ph  ->  ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1441   E.wex 1662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681
This theorem depends on definitions:  df-bi 189  df-ex 1663
This theorem is referenced by: (None)
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