![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > nsyld | Structured version Visualization version GIF version |
Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005.) |
Ref | Expression |
---|---|
nsyld.1 | ⊢ (𝜑 → (𝜓 → ¬ 𝜒)) |
nsyld.2 | ⊢ (𝜑 → (𝜏 → 𝜒)) |
Ref | Expression |
---|---|
nsyld | ⊢ (𝜑 → (𝜓 → ¬ 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nsyld.1 | . 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜒)) | |
2 | nsyld.2 | . . 3 ⊢ (𝜑 → (𝜏 → 𝜒)) | |
3 | 2 | con3d 147 | . 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜏)) |
4 | 1, 3 | syld 46 | 1 ⊢ (𝜑 → (𝜓 → ¬ 𝜏)) |
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: pm2.65d 186 pltn2lp 16792 alexsubALTlem4 21664 ifeqeqx 28745 cvrat 33726 radcnvrat 37535 eupth2eucrct 41385 |
Copyright terms: Public domain | W3C validator |