Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  hbntg Structured version   Unicode version

Theorem hbntg 30038
Description: A more general form of hbnt 1924. (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 1887 . . 3  |-  ( -. 
A. x  -.  A. x ps  ->  ps )
21con1i 131 . 2  |-  ( -. 
ps  ->  A. x  -.  A. x ps )
3 con3 136 . . 3  |-  ( (
ph  ->  A. x ps )  ->  ( -.  A. x ps  ->  -.  ph ) )
43al2imi 1659 . 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 1405
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-12 1880
This theorem depends on definitions:  df-bi 187  df-ex 1636
This theorem is referenced by:  hbimtg  30039  hbng  30041
  Copyright terms: Public domain W3C validator