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Theorem 19.9ht 1532
Description: A closed version of one direction of 19.9 1535. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.9ht  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )

Proof of Theorem 19.9ht
StepHypRef Expression
1 id 19 . . 3  |-  ( ph  ->  ph )
21ax-gen 1338 . 2  |-  A. x
( ph  ->  ph )
3 19.23ht 1386 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( A. x (
ph  ->  ph )  <->  ( E. x ph  ->  ph ) ) )
42, 3mpbii 136 1  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1241   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-gen 1338  ax-ie2 1383
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  19.9t  1533  19.9h  1534  19.9hd  1552
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