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Mirrors > Home > MPE Home > Th. List > mt3i | Structured version Visualization version GIF version |
Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.) |
Ref | Expression |
---|---|
mt3i.1 | ⊢ ¬ 𝜒 |
mt3i.2 | ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) |
Ref | Expression |
---|---|
mt3i | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mt3i.1 | . . 3 ⊢ ¬ 𝜒 | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → ¬ 𝜒) |
3 | mt3i.2 | . 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) | |
4 | 2, 3 | mt3d 150 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: biorfi 938 ordeleqon 7535 wofib 9095 harcard 9493 infpssALT 9826 zorn2lem4 10012 lt6abl 19147 gzrngunitlem 20295 bwth 22174 i1f0rn 24447 dfon2lem3 33348 slerec 33669 poimirlem30 35463 |
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