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Mirrors > Home > ILE Home > Th. List > notnotnot | GIF version |
Description: Triple negation is equivalent to negation. (Contributed by Jim Kingdon, 28-Jul-2018.) |
Ref | Expression |
---|---|
notnotnot | ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 624 | . . 3 ⊢ (𝜑 → ¬ ¬ 𝜑) | |
2 | 1 | con3i 627 | . 2 ⊢ (¬ ¬ ¬ 𝜑 → ¬ 𝜑) |
3 | notnot 624 | . 2 ⊢ (¬ 𝜑 → ¬ ¬ ¬ 𝜑) | |
4 | 2, 3 | impbii 125 | 1 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: stabnot 828 dcnnOLD 844 bj-nnsn 13689 |
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