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| Mirrors > Home > MPE Home > Th. List > mtbird | Structured version Visualization version GIF version | ||
| Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 10-May-1994.) |
| Ref | Expression |
|---|---|
| mtbird.min | ⊢ (𝜑 → ¬ 𝜒) |
| mtbird.maj | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| Ref | Expression |
|---|---|
| mtbird | ⊢ (𝜑 → ¬ 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mtbird.min | . 2 ⊢ (𝜑 → ¬ 𝜒) | |
| 2 | mtbird.maj | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 3 | 2 | biimpd 229 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 4 | 1, 3 | mtod 198 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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