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Theorem hbntg 23330
Description: A more general form of hbnt 1717. (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 ax-6o 1697 . . 3  |-  ( -. 
A. x  -.  A. x ps  ->  ps )
21con1i 123 . 2  |-  ( -. 
ps  ->  A. x  -.  A. x ps )
3 con3 128 . . 3  |-  ( (
ph  ->  A. x ps )  ->  ( -.  A. x ps  ->  -.  ph ) )
43al2imi 1549 . 2  |-  ( A. x ( ph  ->  A. x ps )  -> 
( A. x  -.  A. x ps  ->  A. x  -.  ph ) )
52, 4syl5 30 1  |-  ( A. x ( ph  ->  A. x ps )  -> 
( -.  ps  ->  A. x  -.  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1532
This theorem is referenced by:  hbimtg  23331  hbng  23333
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-6o 1697
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