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Theorem axc7e 1914
Description: Abbreviated version of axc7 1913. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
axc7e  |-  ( E. x A. x ph  ->  ph )

Proof of Theorem axc7e
StepHypRef Expression
1 df-ex 1661 . 2  |-  ( E. x A. x ph  <->  -. 
A. x  -.  A. x ph )
2 axc7 1913 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
31, 2sylbi 199 1  |-  ( E. x A. x ph  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1436   E.wex 1660
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-ex 1661
This theorem is referenced by:  19.9ht  1941
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