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Theorem hbald 1751
Description: Deduction form of bound-variable hypothesis builder hbal 1747. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
hbald.1  |-  ( ph  ->  A. y ph )
hbald.2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
hbald  |-  ( ph  ->  ( A. y ps 
->  A. x A. y ps ) )

Proof of Theorem hbald
StepHypRef Expression
1 hbald.1 . . 3  |-  ( ph  ->  A. y ph )
2 hbald.2 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
31, 2alimdh 1569 . 2  |-  ( ph  ->  ( A. y ps 
->  A. y A. x ps ) )
4 ax-7 1745 . 2  |-  ( A. y A. x ps  ->  A. x A. y ps )
53, 4syl6 31 1  |-  ( ph  ->  ( A. y ps 
->  A. x A. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546
This theorem is referenced by:  nfald  1867  dvelimhwOLD  1873  dvelimvOLD  1994  dvelimhOLD  2018  dvelimALT  2187  dvelimf-o  2234
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-gen 1552  ax-5 1563  ax-7 1745
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