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Theorem hbnd 1590
Description: Deduction form of bound-variable hypothesis builder hbn 1589. (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 1403 . 2  |-  ( ph  ->  A. x ( ps 
->  A. x ps )
)
4 hbnt 1588 . 2  |-  ( A. x ( ps  ->  A. x ps )  -> 
( -.  ps  ->  A. x  -.  ps )
)
53, 4syl 14 1  |-  ( ph  ->  ( -.  ps  ->  A. x  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1287
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-in1 579  ax-in2 580  ax-5 1381  ax-gen 1383  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295
This theorem is referenced by: (None)
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