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Theorem exisym1 26122
Description: A symmetry with  E..

See negsym1 26115 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
exisym1  |-  ( E. x E. x  F.  ->  E. x ph )

Proof of Theorem exisym1
StepHypRef Expression
1 nfe1 1747 . 2  |-  F/ x E. x ph
2 falim 1337 . . 3  |-  (  F. 
->  ph )
32eximi 1585 . 2  |-  ( E. x  F.  ->  E. x ph )
41, 3exlimi 1821 1  |-  ( E. x E. x  F.  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    F. wfal 1326   E.wex 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-tru 1328  df-fal 1329  df-ex 1551  df-nf 1554
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