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Theorem hbimd 1835
Description: Deduction form of bound-variable hypothesis builder hbim 1837. (Contributed by NM, 1-Jan-2002.) (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 1784 . . 3  |-  ( ph  ->  F/ x ps )
4 hbimd.3 . . . 4  |-  ( ph  ->  ( ch  ->  A. x ch ) )
51, 4nfdh 1784 . . 3  |-  ( ph  ->  F/ x ch )
63, 5nfimd 1828 . 2  |-  ( ph  ->  F/ x ( ps 
->  ch ) )
76nfrd 1780 1  |-  ( ph  ->  ( ( ps  ->  ch )  ->  A. x
( ps  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550
This theorem is referenced by:  spimehOLD  1841  dvelimhwOLD  1878  dvelimvOLD  2029  dvelimhOLD  2073  dvelimALT  2211  dvelimf-o  2258  dvelimhwNEW7  29456  dvelimvNEW7  29463  dvelimhvAUX7  29493  dvelimALTNEW7  29637  dvelimhOLD7  29714
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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