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Theorem pm2.65d 178
Description: Deduction rule for proof by contradiction. (Contributed by NM, 26-Jun-1994.) (Proof shortened by Wolf Lammen, 26-May-2013.)
Hypotheses
Ref Expression
pm2.65d.1  |-  ( ph  ->  ( ps  ->  ch ) )
pm2.65d.2  |-  ( ph  ->  ( ps  ->  -.  ch ) )
Assertion
Ref Expression
pm2.65d  |-  ( ph  ->  -.  ps )

Proof of Theorem pm2.65d
StepHypRef Expression
1 pm2.65d.2 . . 3  |-  ( ph  ->  ( ps  ->  -.  ch ) )
2 pm2.65d.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2nsyld 145 . 2  |-  ( ph  ->  ( ps  ->  -.  ps ) )
43pm2.01d 172 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  mtod  180  pm2.65da  578  unxpdomlem2  7725  cardlim  8353  winainflem  9064  winalim2  9067  discr  12354  sqrmo  13254  vdwnnlem3  14885  nmlno0lem  26371  nmlnop0iALT  27585  iooelexlt  31672
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