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Theorem wl-lem-nexmo 30259
Description: This theorem provides a basic working step in proving theorems about  E* or  E!. (Contributed by Wolf Lammen, 3-Oct-2019.)
Assertion
Ref Expression
wl-lem-nexmo  |-  ( -. 
E. x ph  ->  A. x ( ph  ->  x  =  z ) )

Proof of Theorem wl-lem-nexmo
StepHypRef Expression
1 alnex 1619 . 2  |-  ( A. x  -.  ph  <->  -.  E. x ph )
2 pm2.21 108 . . 3  |-  ( -. 
ph  ->  ( ph  ->  x  =  z ) )
32alimi 1638 . 2  |-  ( A. x  -.  ph  ->  A. x
( ph  ->  x  =  z ) )
41, 3sylbir 213 1  |-  ( -. 
E. x ph  ->  A. x ( ph  ->  x  =  z ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by: (None)
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