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Theorem dfnot 1651
Description: Given falsum , we can define the negation of a wff 𝜑 as the statement that follows from assuming 𝜑. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof shortened by Wolf Lammen, 21-Jul-2019.)
Assertion
Ref Expression
dfnot 𝜑 ↔ (𝜑 → ⊥))

Proof of Theorem dfnot
StepHypRef Expression
1 fal 1639 . 2 ¬ ⊥
2 mtt 353 . 2 (¬ ⊥ → (¬ 𝜑 ↔ (𝜑 → ⊥)))
31, 2ax-mp 5 1 𝜑 ↔ (𝜑 → ⊥))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wfal 1637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-tru 1635  df-fal 1638
This theorem is referenced by:  inegd  1652  bj-godellob  32896
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