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Theorem pm2.18 102
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 pm2.21 100 . . . 4  |-  ( -. 
ph  ->  ( ph  ->  -.  ( -.  ph  ->  ph ) ) )
21a2i 12 . . 3  |-  ( ( -.  ph  ->  ph )  ->  ( -.  ph  ->  -.  ( -.  ph  ->  ph ) ) )
32con4d 97 . 2  |-  ( ( -.  ph  ->  ph )  ->  ( ( -.  ph  ->  ph )  ->  ph )
)
43pm2.43i 43 1  |-  ( ( -.  ph  ->  ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  pm2.18d  103  pm4.81  355  ax10  1884  sumdmdlem2  22999
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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