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Mirrors > Home > MPE Home > Th. List > nanor | Structured version Visualization version GIF version |
Description: Alternative denial in terms of disjunction and negation. This explains the name "alternative denial". (Contributed by BJ, 19-Oct-2022.) |
Ref | Expression |
---|---|
nanor | ⊢ ((𝜑 ⊼ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nan 1482 | . 2 ⊢ ((𝜑 ⊼ 𝜓) ↔ ¬ (𝜑 ∧ 𝜓)) | |
2 | ianor 978 | . 2 ⊢ (¬ (𝜑 ∧ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)) | |
3 | 1, 2 | bitri 277 | 1 ⊢ ((𝜑 ⊼ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 208 ∧ wa 398 ∨ wo 843 ⊼ wnan 1481 |
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 209 df-an 399 df-or 844 df-nan 1482 |
This theorem is referenced by: elnanelprv 32676 |
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