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Theorem 19.9hd 1640
Description: A deduction version of one direction of 19.9 1623. This is an older variation of this theorem; new proofs should use 19.9d 1639. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)
Hypotheses
Ref Expression
19.9hd.1  |-  ( ps 
->  A. x ps )
19.9hd.2  |-  ( ps 
->  ( ph  ->  A. x ph ) )
Assertion
Ref Expression
19.9hd  |-  ( ps 
->  ( E. x ph  ->  ph ) )

Proof of Theorem 19.9hd
StepHypRef Expression
1 19.9hd.1 . 2  |-  ( ps 
->  A. x ps )
2 19.9hd.2 . . 3  |-  ( ps 
->  ( ph  ->  A. x ph ) )
32alimi 1431 . 2  |-  ( A. x ps  ->  A. x
( ph  ->  A. x ph ) )
4 19.9ht 1620 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )
51, 3, 43syl 17 1  |-  ( ps 
->  ( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1329   E.wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1423  ax-gen 1425  ax-ie2 1470
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  sbiedh  1760  bj-sbimedh  13122
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