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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 ((¬ φφ) → φ)

Proof of Theorem pm2.18
StepHypRef Expression
1 pm2.21 100 . . . 4 φ → (φ → ¬ (¬ φφ)))
21a2i 12 . . 3 ((¬ φφ) → (¬ φ → ¬ (¬ φφ)))
32con4d 97 . 2 ((¬ φφ) → ((¬ φφ) → φ))
43pm2.43i 43 1 ((¬ φφ) → φ)
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:  pm2.18d  103  pm4.81  355  ax10  1944
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