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Theorem exisym1 24935
Description: A symmetry with  E..

See negsym1 24928 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 1718 . 2  |-  F/ x E. x ph
2 falim 1319 . . 3  |-  (  F. 
->  ph )
32eximi 1566 . 2  |-  ( E. x  F.  ->  E. x ph )
41, 3exlimi 1813 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
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-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-fal 1311  df-ex 1532  df-nf 1535
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