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Mirrors > Home > MPE Home > Th. List > Mathboxes > 3pm3.2ni | Structured version Visualization version GIF version |
Description: Triple negated disjunction introduction. (Contributed by Scott Fenton, 20-Apr-2011.) |
Ref | Expression |
---|---|
3pm3.2ni.1 | ⊢ ¬ 𝜑 |
3pm3.2ni.2 | ⊢ ¬ 𝜓 |
3pm3.2ni.3 | ⊢ ¬ 𝜒 |
Ref | Expression |
---|---|
3pm3.2ni | ⊢ ¬ (𝜑 ∨ 𝜓 ∨ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3pm3.2ni.1 | . . . 4 ⊢ ¬ 𝜑 | |
2 | 3pm3.2ni.2 | . . . 4 ⊢ ¬ 𝜓 | |
3 | 1, 2 | pm3.2ni 878 | . . 3 ⊢ ¬ (𝜑 ∨ 𝜓) |
4 | 3pm3.2ni.3 | . . 3 ⊢ ¬ 𝜒 | |
5 | 3, 4 | pm3.2ni 878 | . 2 ⊢ ¬ ((𝜑 ∨ 𝜓) ∨ 𝜒) |
6 | df-3or 1087 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒)) | |
7 | 5, 6 | mtbir 323 | 1 ⊢ ¬ (𝜑 ∨ 𝜓 ∨ 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 844 ∨ w3o 1085 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-or 845 df-3or 1087 |
This theorem is referenced by: poxp3 33792 sltsolem1 33874 |
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