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Theorem exisym1 26179
Description: A symmetry with  E..

See negsym1 26172 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 1748 . 2  |-  F/ x E. x ph
2 falim 1338 . . 3  |-  (  F. 
->  ph )
32eximi 1586 . 2  |-  ( E. x  F.  ->  E. x ph )
41, 3exlimi 1822 1  |-  ( E. x E. x  F.  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    F. wfal 1327   E.wex 1551
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-tru 1329  df-fal 1330  df-ex 1552  df-nf 1555
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