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Theorem 19.9ht 1548
Description: A closed version of one direction of 19.9 1551. (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 1354 . 2  |-  A. x
( ph  ->  ph )
3 19.23ht 1402 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( A. x (
ph  ->  ph )  <->  ( E. x ph  ->  ph ) ) )
42, 3mpbii 140 1  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1257   E.wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-gen 1354  ax-ie2 1399
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  19.9t  1549  19.9h  1550  19.9hd  1568
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