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Theorem hbng 24165
Description: A more general form of hbn 1720. (Contributed by Scott Fenton, 13-Dec-2010.)
Hypothesis
Ref Expression
hbg.1  |-  ( ph  ->  A. x ps )
Assertion
Ref Expression
hbng  |-  ( -. 
ps  ->  A. x  -.  ph )

Proof of Theorem hbng
StepHypRef Expression
1 hbntg 24162 . 2  |-  ( A. x ( ph  ->  A. x ps )  -> 
( -.  ps  ->  A. x  -.  ph )
)
2 hbg.1 . 2  |-  ( ph  ->  A. x ps )
31, 2mpg 1535 1  |-  ( -. 
ps  ->  A. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
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