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Theorem hbe1 1746
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 1551 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
2 hbn1 1745 . 2  |-  ( -. 
A. x  -.  ph  ->  A. x  -.  A. x  -.  ph )
31, 2hbxfrbi 1577 1  |-  ( E. x ph  ->  A. x E. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549   E.wex 1550
This theorem is referenced by:  nfe1  1747  hba1  1804  19.23hOLD  1839  equs5e  1910  ax12olem5OLD  2015  ax10lem2OLD  2026  axie1  2411  exlimexi  28608  vk15.4j  28612  vk15.4jVD  29026
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-6 1744
This theorem depends on definitions:  df-bi 178  df-ex 1551
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