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Theorem pm2.18 120
Description: Proof by contradiction. Theorem *2.18 of [WhiteheadRussell] p. 103. Also called the Law of Clavius. See also pm2.01 178. (Contributed by NM, 29-Dec-1992.)
Assertion
Ref Expression
pm2.18 ((¬ 𝜑𝜑) → 𝜑)

Proof of Theorem pm2.18
StepHypRef Expression
1 pm2.21 118 . . . 4 𝜑 → (𝜑 → ¬ (¬ 𝜑𝜑)))
21a2i 14 . . 3 ((¬ 𝜑𝜑) → (¬ 𝜑 → ¬ (¬ 𝜑𝜑)))
32con4d 112 . 2 ((¬ 𝜑𝜑) → ((¬ 𝜑𝜑) → 𝜑))
43pm2.43i 49 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:  pm2.18i  121  pm2.18d  122  pm4.81  379  sumdmdlem2  28468  pm4.81ALT  31522  axc11n11r  31666
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