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Theorem hbe1 1749
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 1552 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
2 hbn1 1748 . 2  |-  ( -. 
A. x  -.  ph  ->  A. x  -.  A. x  -.  ph )
31, 2hbxfrbi 1578 1  |-  ( E. x ph  ->  A. x E. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1550   E.wex 1551
This theorem is referenced by:  nfe1  1750  hba1  1807  19.23hOLD  1842  equs5e  1914  ax12olem5OLD  2019  ax10lem2OLD  2030  axie1  2418  ac6s6  26800  exlimexi  28780  vk15.4j  28784  vk15.4jVD  29200
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-6 1747
This theorem depends on definitions:  df-bi 179  df-ex 1552
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