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Theorem unqsym1 24936
Description: A symmetry with  E!.

See negsym1 24928 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 24918 . . . 4  |-  -.  E! x  F.
21nex 1545 . . 3  |-  -.  E. x E! x  F.
3 euex 2179 . . 3  |-  ( E! x E! x  F.  ->  E. x E! x  F.  )
42, 3mto 167 . 2  |-  -.  E! x E! x  F.
54pm2.21i 123 1  |-  ( E! x E! x  F.  ->  E! x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    F. wfal 1308   E.wex 1531   E!weu 2156
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-fal 1311  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160
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