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| Mirrors > Home > MPE Home > Th. List > imnan | Structured version Visualization version GIF version | ||
| Description: Express an implication in terms of a negated conjunction. (Contributed by NM, 9-Apr-1994.) |
| Ref | Expression |
|---|---|
| imnan | ⊢ ((𝜑 → ¬ 𝜓) ↔ ¬ (𝜑 ∧ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-an 396 | . 2 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓)) | |
| 2 | 1 | con2bii 357 | 1 ⊢ ((𝜑 → ¬ 𝜓) ↔ ¬ (𝜑 ∧ 𝜓)) |
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