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Mirrors > Home > ILE Home > Th. List > notnotnot | GIF version |
Description: Triple negation. (Contributed by Jim Kingdon, 28-Jul-2018.) |
Ref | Expression |
---|---|
notnotnot | ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 559 | . . 3 ⊢ (𝜑 → ¬ ¬ 𝜑) | |
2 | 1 | con3i 562 | . 2 ⊢ (¬ ¬ ¬ 𝜑 → ¬ 𝜑) |
3 | notnot 559 | . 2 ⊢ (¬ 𝜑 → ¬ ¬ ¬ 𝜑) | |
4 | 2, 3 | impbii 117 | 1 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: stabnot 741 testbitestn 823 |
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