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Theorem hbnd 1824
Description: Deduction form of bound-variable hypothesis builder hbn 1720. (Contributed by NM, 3-Jan-2002.)
Hypotheses
Ref Expression
hbnd.1  |-  ( ph  ->  A. x ph )
hbnd.2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
hbnd  |-  ( ph  ->  ( -.  ps  ->  A. x  -.  ps )
)

Proof of Theorem hbnd
StepHypRef Expression
1 hbnd.1 . . 3  |-  ( ph  ->  A. x ph )
2 hbnd.2 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
31, 2alrimih 1552 . 2  |-  ( ph  ->  A. x ( ps 
->  A. x ps )
)
4 hbnt 1724 . 2  |-  ( A. x ( ps  ->  A. x ps )  -> 
( -.  ps  ->  A. x  -.  ps )
)
53, 4syl 15 1  |-  ( ph  ->  ( -.  ps  ->  A. x  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem is referenced by:  a12studyALT  29133
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
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