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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nndcALT | GIF version |
Description: Alternate proof of nndc 846. (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by BJ, 9-Oct-2019.) |
Ref | Expression |
---|---|
bj-nndcALT | ⊢ ¬ ¬ DECID 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 624 | . . 3 ⊢ (¬ 𝜑 → ¬ ¬ ¬ 𝜑) | |
2 | bj-nnor 13690 | . . 3 ⊢ (¬ ¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 → ¬ ¬ ¬ 𝜑)) | |
3 | 1, 2 | mpbir 145 | . 2 ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑) |
4 | df-dc 830 | . . 3 ⊢ (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑)) | |
5 | 4 | notbii 663 | . 2 ⊢ (¬ DECID 𝜑 ↔ ¬ (𝜑 ∨ ¬ 𝜑)) |
6 | 3, 5 | mtbir 666 | 1 ⊢ ¬ ¬ DECID 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 703 DECID wdc 829 |
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 df-dc 830 |
This theorem is referenced by: (None) |
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