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Theorem hbexd 1627
Description: Deduction form of bound-variable hypothesis builder hbex 1570. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
hbexd.1  |-  ( ph  ->  A. y ph )
hbexd.2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
hbexd  |-  ( ph  ->  ( E. y ps 
->  A. x E. y ps ) )

Proof of Theorem hbexd
StepHypRef Expression
1 hbexd.1 . . 3  |-  ( ph  ->  A. y ph )
2 hbexd.2 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
31, 2eximdh 1545 . 2  |-  ( ph  ->  ( E. y ps 
->  E. y A. x ps ) )
4 19.12 1598 . 2  |-  ( E. y A. x ps 
->  A. x E. y ps )
53, 4syl6 33 1  |-  ( ph  ->  ( E. y ps 
->  A. x E. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1285   E.wex 1424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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