| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > pm4.71rd | Structured version Visualization version GIF version | ||
| Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by NM, 10-Feb-2005.) |
| Ref | Expression |
|---|---|
| pm4.71rd.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| pm4.71rd | ⊢ (𝜑 → (𝜓 ↔ (𝜒 ∧ 𝜓))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm4.71rd.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 2 | 1 | pm4.71d 561 | . 2 ⊢ (𝜑 → (𝜓 ↔ (𝜓 ∧ 𝜒))) |
| 3 | 2 | biancomd 463 | 1 ⊢ (𝜑 → (𝜓 ↔ (𝜒 ∧ 𝜓))) |
| Copyright terms: Public domain | W3C validator |