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| Mirrors > Home > MPE Home > Th. List > ianor | Structured version Visualization version GIF version | ||
| Description: Negated conjunction in terms of disjunction (De Morgan's law). Theorem *4.51 of [WhiteheadRussell] p. 120. (Contributed by NM, 14-May-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.) |
| Ref | Expression |
|---|---|
| ianor | ⊢ (¬ (𝜑 ∧ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imnan 399 | . 2 ⊢ ((𝜑 → ¬ 𝜓) ↔ ¬ (𝜑 ∧ 𝜓)) | |
| 2 | pm4.62 857 | . 2 ⊢ ((𝜑 → ¬ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)) | |
| 3 | 1, 2 | bitr3i 277 | 1 ⊢ (¬ (𝜑 ∧ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)) |
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