| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > biimpa | Structured version Visualization version GIF version | ||
| Description: Importation inference from a logical equivalence. (Contributed by NM, 3-May-1994.) |
| Ref | Expression |
|---|---|
| biimpa.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| Ref | Expression |
|---|---|
| biimpa | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimpa.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 2 | 1 | biimpd 229 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 3 | 2 | imp 406 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Copyright terms: Public domain | W3C validator |