| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > mpbiri | Structured version Visualization version GIF version | ||
| Description: An inference from a nested biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 25-Oct-2012.) |
| Ref | Expression |
|---|---|
| mpbiri.min | ⊢ 𝜒 |
| mpbiri.maj | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| Ref | Expression |
|---|---|
| mpbiri | ⊢ (𝜑 → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpbiri.min | . . 3 ⊢ 𝜒 | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → 𝜒) |
| 3 | mpbiri.maj | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 4 | 2, 3 | mpbird 257 | 1 ⊢ (𝜑 → 𝜓) |
| Copyright terms: Public domain | W3C validator |