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Theorem 19.9ht 1792
Description: A closed version of 19.9 1797. (Contributed by NM, 5-Aug-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 1584 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  E. x A. x ph ) )
2 a6e 1767 . 2  |-  ( E. x A. x ph  ->  ph )
31, 2syl6 31 1  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   E.wex 1550
This theorem is referenced by:  19.9t  1793  19.9hOLD  1795  hbnt  1799
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-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551
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