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Theorem a6e 1755
Description: Abbreviated version of ax6o 1723. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
a6e  |-  ( E. x A. x ph  ->  ph )

Proof of Theorem a6e
StepHypRef Expression
1 df-ex 1529 . 2  |-  ( E. x A. x ph  <->  -. 
A. x  -.  A. x ph )
2 ax6o 1723 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
31, 2sylbi 187 1  |-  ( E. x A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-ex 1529
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