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Theorem pm2.18 104
Description: Proof by contradiction. Theorem *2.18 of [WhiteheadRussell] p. 103. Also called the Law of Clavius. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pm2.18  |-  ( ( -.  ph  ->  ph )  ->  ph )

Proof of Theorem pm2.18
StepHypRef Expression
1 pm2.21 102 . . . 4  |-  ( -. 
ph  ->  ( ph  ->  -.  ( -.  ph  ->  ph ) ) )
21a2i 14 . . 3  |-  ( ( -.  ph  ->  ph )  ->  ( -.  ph  ->  -.  ( -.  ph  ->  ph ) ) )
32con4d 99 . 2  |-  ( ( -.  ph  ->  ph )  ->  ( ( -.  ph  ->  ph )  ->  ph )
)
43pm2.43i 45 1  |-  ( ( -.  ph  ->  ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6
This theorem is referenced by:  pm2.18d  105  pm4.81  357  ax10  1677  sumdmdlem2  22829
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
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