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Theorem notnotri 126
 Description: Inference associated with notnotr 125. Remark: the proof via notnotr 125 and ax-mp 5 also has three essential steps, but has a total number of steps equal to 8, instead of the present 7, because it has to construct the formula 𝜑 twice and the formula ¬ ¬ 𝜑, whereas the present proof has to construct the formula 𝜑 twice and the formula ¬ 𝜑, and therefore makes only one use of wn 3 instead of two. This can be checked by running the Metamath command "SHOW PROOF notnotri / NORMAL". (Contributed by NM, 27-Feb-2008.) (Proof shortened by Wolf Lammen, 15-Jul-2021.)
Hypothesis
Ref Expression
notnotri.1 ¬ ¬ 𝜑
Assertion
Ref Expression
notnotri 𝜑

Proof of Theorem notnotri
StepHypRef Expression
1 notnotri.1 . . 3 ¬ ¬ 𝜑
21pm2.21i 116 . 2 𝜑𝜑)
32pm2.18i 123 1 𝜑
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem is referenced by:  mt3  192  pm2.65ni  38728
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