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Theorem exisym1 31090
Description: A symmetry with  E..

See negsym1 31083 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 1894 . 2  |-  F/ x E. x ph
2 falim 1451 . . 3  |-  ( F. 
->  ph )
32eximi 1701 . 2  |-  ( E. x F.  ->  E. x ph )
41, 3exlimi 1972 1  |-  ( E. x E. x F.  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   F. wfal 1442   E.wex 1657
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-tru 1440  df-fal 1443  df-ex 1658  df-nf 1662
This theorem is referenced by: (None)
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