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Theorem hbntg 25433
Description: A more general form of hbnt 1799. (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 ax6o 1766 . . 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 1570 . 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 3    -> wi 4   A.wal 1549
This theorem is referenced by:  hbimtg  25434  hbng  25436
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551
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