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| Mirrors > Home > MPE Home > Th. List > notbid | Structured version Visualization version GIF version | ||
| Description: Deduction negating both sides of a logical equivalence. (Contributed by NM, 21-May-1994.) |
| Ref | Expression |
|---|---|
| notbid.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| Ref | Expression |
|---|---|
| notbid | ⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | notbid.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 2 | notnotb 315 | . . 3 ⊢ (𝜓 ↔ ¬ ¬ 𝜓) | |
| 3 | notnotb 315 | . . 3 ⊢ (𝜒 ↔ ¬ ¬ 𝜒) | |
| 4 | 1, 2, 3 | 3bitr3g 313 | . 2 ⊢ (𝜑 → (¬ ¬ 𝜓 ↔ ¬ ¬ 𝜒)) |
| 5 | 4 | con4bid 317 | 1 ⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒)) |
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