![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > Mathboxes > nnexmid | GIF version |
Description: Double negation of excluded middle. Intuitionistic logic refutes the negation of excluded middle (but, of course, does not prove excluded middle) for any formula. (Contributed by BJ, 9-Oct-2019.) |
Ref | Expression |
---|---|
nnexmid | ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.24 660 | . 2 ⊢ ¬ (¬ 𝜑 ∧ ¬ ¬ 𝜑) | |
2 | ioran 702 | . 2 ⊢ (¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∧ ¬ ¬ 𝜑)) | |
3 | 1, 2 | mtbir 629 | 1 ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∧ wa 102 ∨ wo 662 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: nndc 10815 |
Copyright terms: Public domain | W3C validator |