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Mirrors > Home > ILE Home > Th. List > nnexmid | GIF version |
Description: Double negation of decidability of a formula. See also comment of nndc 846 to avoid a pitfall that could come from the label "nnexmid". This theorem can also be proved from bj-nnor 13690 as in bj-nndcALT 13714. (Contributed by BJ, 9-Oct-2019.) |
Ref | Expression |
---|---|
nnexmid | ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.24 688 | . 2 ⊢ ¬ (¬ 𝜑 ∧ ¬ ¬ 𝜑) | |
2 | ioran 747 | . 2 ⊢ (¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∧ ¬ ¬ 𝜑)) | |
3 | 1, 2 | mtbir 666 | 1 ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∧ wa 103 ∨ wo 703 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: nndc 846 exmid1stab 13955 |
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