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Mirrors > Home > MPE Home > Th. List > notnotri | Structured version Visualization version GIF version |
Description: Inference associated with notnotr 130. For a shorter proof using ax-2 7, see notnotriALT 132. (Contributed by NM, 27-Feb-2008.) (Proof shortened by Wolf Lammen, 15-Jul-2021.) Remove dependency on ax-2 7. (Revised by Steven Nguyen, 27-Dec-2022.) |
Ref | Expression |
---|---|
notnotri.1 | ⊢ ¬ ¬ 𝜑 |
Ref | Expression |
---|---|
notnotri | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotri.1 | . 2 ⊢ ¬ ¬ 𝜑 | |
2 | 1 | pm2.21i 119 | . 2 ⊢ (¬ 𝜑 → ¬ ¬ ¬ 𝜑) |
3 | 1, 2 | mt4 116 | 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-3 8 |
This theorem is referenced by: mt3 200 pm2.65ni 42562 |
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