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Theorem hbe1 1847
Description:  x is not free in  E. x ph. (Contributed by NM, 24-Jan-1993.)
Assertion
Ref Expression
hbe1  |-  ( E. x ph  ->  A. x E. x ph )

Proof of Theorem hbe1
StepHypRef Expression
1 df-ex 1621 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
2 hbn1 1846 . 2  |-  ( -. 
A. x  -.  ph  ->  A. x  -.  A. x  -.  ph )
31, 2hbxfrbi 1651 1  |-  ( E. x ph  ->  A. x E. x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1397   E.wex 1620
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-10 1845
This theorem depends on definitions:  df-bi 185  df-ex 1621
This theorem is referenced by:  nfe1  1848  hba1  1904  equs5e  1987  axie1  2354  ac6s6  30746  exlimexi  33627  vk15.4j  33631  vk15.4jVD  34061
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