Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 148 | 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 936 ordeleqon 7632 wofib 9304 harcard 9736 infpssALT 10069 zorn2lem4 10255 lt6abl 19496 gzrngunitlem 20663 bwth 22561 i1f0rn 24846 dfon2lem3 33761 slerec 34013 poimirlem30 35807 |
Copyright terms: Public domain | W3C validator |