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Theorem 19.9ht 1944
Description: A closed version of 19.9 1947. (Contributed by NM, 13-May-1993.) (Proof shortened by Wolf Lammen, 3-Mar-2018.)
Assertion
Ref Expression
19.9ht  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )

Proof of Theorem 19.9ht
StepHypRef Expression
1 exim 1700 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  E. x A. x ph ) )
2 axc7e 1917 . 2  |-  ( E. x A. x ph  ->  ph )
31, 2syl6 34 1  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   E.wex 1657
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658
This theorem is referenced by:  19.9d  1945  19.9tOLD  1949  hbnt  1953  bj-19.9htbi  31257
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