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Mirrors > Home > MPE Home > Th. List > mtbid | Structured version Visualization version GIF version |
Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995.) |
Ref | Expression |
---|---|
mtbid.min | ⊢ (𝜑 → ¬ 𝜓) |
mtbid.maj | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
mtbid | ⊢ (𝜑 → ¬ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mtbid.min | . 2 ⊢ (𝜑 → ¬ 𝜓) | |
2 | mtbid.maj | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 2 | biimprd 251 | . 2 ⊢ (𝜑 → (𝜒 → 𝜓)) |
4 | 1, 3 | mtod 201 | 1 ⊢ (𝜑 → ¬ 𝜒) |
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