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| Mirrors > Home > MPE Home > Th. List > notbii | Structured version Visualization version GIF version | ||
| Description: Negate both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 19-May-2013.) |
| Ref | Expression |
|---|---|
| notbii.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| notbii | ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | notbii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | notbi 319 | . 2 ⊢ ((𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ ¬ 𝜓)) | |
| 3 | 1, 2 | mpbi 230 | 1 ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
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