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Theorem bj-nimn 32526
Description: If a formula is true, then it does not imply its negation. (Contributed by BJ, 19-Mar-2020.) A shorter proof is possible using id 22 and jc 159, however, the present proof uses theorems that are more basic than jc 159. (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nimn (𝜑 → ¬ (𝜑 → ¬ 𝜑))

Proof of Theorem bj-nimn
StepHypRef Expression
1 pm2.01 180 . 2 ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
21con2i 134 1 (𝜑 → ¬ (𝜑 → ¬ 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:  bj-nimni  32527
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