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| Mirrors > Home > MPE Home > Th. List > mtbiri | Structured version Visualization version GIF version | ||
| Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 24-Aug-1995.) |
| Ref | Expression |
|---|---|
| mtbiri.min | ⊢ ¬ 𝜒 |
| mtbiri.maj | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| Ref | Expression |
|---|---|
| mtbiri | ⊢ (𝜑 → ¬ 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mtbiri.min | . 2 ⊢ ¬ 𝜒 | |
| 2 | mtbiri.maj | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 3 | 2 | biimpd 229 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 4 | 1, 3 | mtoi 199 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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