![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > 3impib | Structured version Visualization version GIF version |
Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.) |
Ref | Expression |
---|---|
3impib.1 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Ref | Expression |
---|---|
3impib | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3impib.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) | |
2 | 1 | expd 451 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | 3imp 1249 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Copyright terms: Public domain | W3C validator |