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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 852 to avoid a pitfall that could come from the label "nnexmid". This theorem can also be proved from bj-nnor 14944 as in bj-nndcALT 14968. (Contributed by BJ, 9-Oct-2019.) |
Ref | Expression |
---|---|
nnexmid | ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.24 694 | . 2 ⊢ ¬ (¬ 𝜑 ∧ ¬ ¬ 𝜑) | |
2 | ioran 753 | . 2 ⊢ (¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∧ ¬ ¬ 𝜑)) | |
3 | 1, 2 | mtbir 672 | 1 ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∧ wa 104 ∨ wo 709 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: nndc 852 exmid1stab 4226 |
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