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Theorem hbntg 28815
Description: A more general form of hbnt 1842. (Contributed by Scott Fenton, 13-Dec-2010.)
Assertion
Ref Expression
hbntg  |-  ( A. x ( ph  ->  A. x ps )  -> 
( -.  ps  ->  A. x  -.  ph )
)

Proof of Theorem hbntg
StepHypRef Expression
1 axc7 1810 . . 3  |-  ( -. 
A. x  -.  A. x ps  ->  ps )
21con1i 129 . 2  |-  ( -. 
ps  ->  A. x  -.  A. x ps )
3 con3 134 . . 3  |-  ( (
ph  ->  A. x ps )  ->  ( -.  A. x ps  ->  -.  ph ) )
43al2imi 1616 . 2  |-  ( A. x ( ph  ->  A. x ps )  -> 
( A. x  -.  A. x ps  ->  A. x  -.  ph ) )
52, 4syl5 32 1  |-  ( A. x ( ph  ->  A. x ps )  -> 
( -.  ps  ->  A. x  -.  ph )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1377
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  hbimtg  28816  hbng  28818
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