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Mirrors > Home > ILE Home > Th. List > mtbiri | 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 143 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
4 | 1, 3 | mtoi 659 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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