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Theorem hbe1 1717
Description:  x is not free in  E. x ph. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbe1  |-  ( E. x ph  ->  A. x E. x ph )

Proof of Theorem hbe1
StepHypRef Expression
1 df-ex 1532 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
2 hbn1 1716 . 2  |-  ( -. 
A. x  -.  ph  ->  A. x  -.  A. x  -.  ph )
31, 2hbxfrbi 1558 1  |-  ( E. x ph  ->  A. x E. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530   E.wex 1531
This theorem is referenced by:  nfe1  1718  19.23h  1740  ax12olem5  1884  ax10lem2  1890  exlimexi  28586  vk15.4j  28590  vk15.4jVD  29006  a12study5rev  29744  a12study10  29758  a12study10n  29759  ax9lem15  29776
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-6 1715
This theorem depends on definitions:  df-bi 177  df-ex 1532
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