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Theorem pm2.18 113
Description: Proof by contradiction. Theorem *2.18 of [WhiteheadRussell] p. 103. Also called the Law of Clavius. See also pm2.01 173. (Contributed by NM, 29-Dec-1992.)
Assertion
Ref Expression
pm2.18  |-  ( ( -.  ph  ->  ph )  ->  ph )

Proof of Theorem pm2.18
StepHypRef Expression
1 pm2.21 111 . . . 4  |-  ( -. 
ph  ->  ( ph  ->  -.  ( -.  ph  ->  ph ) ) )
21a2i 14 . . 3  |-  ( ( -.  ph  ->  ph )  ->  ( -.  ph  ->  -.  ( -.  ph  ->  ph ) ) )
32con4d 108 . 2  |-  ( ( -.  ph  ->  ph )  ->  ( ( -.  ph  ->  ph )  ->  ph )
)
43pm2.43i 48 1  |-  ( ( -.  ph  ->  ph )  ->  ph )
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:  pm2.18i  114  pm2.18d  115  pm4.81  373  sumdmdlem2  28153  pm4.81ALT  31200
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