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Theorem hbimd 1859
Description: Deduction form of bound-variable hypothesis builder hbim 1860. (Contributed by NM, 14-May-1993.) (Proof shortened by Wolf Lammen, 3-Jan-2018.)
Hypotheses
Ref Expression
hbimd.1  |-  ( ph  ->  A. x ph )
hbimd.2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
hbimd.3  |-  ( ph  ->  ( ch  ->  A. x ch ) )
Assertion
Ref Expression
hbimd  |-  ( ph  ->  ( ( ps  ->  ch )  ->  A. x
( ps  ->  ch ) ) )

Proof of Theorem hbimd
StepHypRef Expression
1 hbimd.1 . . . 4  |-  ( ph  ->  A. x ph )
2 hbimd.2 . . . 4  |-  ( ph  ->  ( ps  ->  A. x ps ) )
31, 2nfdh 1818 . . 3  |-  ( ph  ->  F/ x ps )
4 hbimd.3 . . . 4  |-  ( ph  ->  ( ch  ->  A. x ch ) )
51, 4nfdh 1818 . . 3  |-  ( ph  ->  F/ x ch )
63, 5nfimd 1855 . 2  |-  ( ph  ->  F/ x ( ps 
->  ch ) )
76nfrd 1814 1  |-  ( ph  ->  ( ( ps  ->  ch )  ->  A. x
( ps  ->  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nf 1591
This theorem is referenced by:  dvelimf-o  2239
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