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Theorem unqsym1 30644
Description: A symmetry with  E!.

See negsym1 30636 for more information. (Contributed by Anthony Hart, 6-Sep-2011.)

Assertion
Ref Expression
unqsym1  |-  ( E! x E! x F.  ->  E! x ph )

Proof of Theorem unqsym1
StepHypRef Expression
1 unnf 30626 . . . 4  |-  -.  E! x F.
21nex 1648 . . 3  |-  -.  E. x E! x F.
3 euex 2264 . . 3  |-  ( E! x E! x F.  ->  E. x E! x F.  )
42, 3mto 176 . 2  |-  -.  E! x E! x F.
54pm2.21i 131 1  |-  ( E! x E! x F.  ->  E! x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   F. wfal 1410   E.wex 1633   E!weu 2238
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771
This theorem depends on definitions:  df-bi 185  df-tru 1408  df-fal 1411  df-ex 1634  df-eu 2242
This theorem is referenced by: (None)
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