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Theorem hbntg 30444
Description: A more general form of hbnt 1949. (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 1912 . . 3  |-  ( -. 
A. x  -.  A. x ps  ->  ps )
21con1i 132 . 2  |-  ( -. 
ps  ->  A. x  -.  A. x ps )
3 con3 139 . . 3  |-  ( (
ph  ->  A. x ps )  ->  ( -.  A. x ps  ->  -.  ph ) )
43al2imi 1683 . 2  |-  ( A. x ( ph  ->  A. x ps )  -> 
( A. x  -.  A. x ps  ->  A. x  -.  ph ) )
52, 4syl5 33 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 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-12 1905
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  hbimtg  30445  hbng  30447
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