| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > simprd | Structured version Visualization version GIF version | ||
| Description: Deduction eliminating a conjunct. (Contributed by NM, 14-May-1993.) A translation of natural deduction rule ∧ ER (∧ elimination right), see natded 30422. (Proof shortened by Wolf Lammen, 3-Oct-2013.) |
| Ref | Expression |
|---|---|
| simprd.1 | ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
| Ref | Expression |
|---|---|
| simprd | ⊢ (𝜑 → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simprd.1 | . . 3 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) | |
| 2 | 1 | ancomd 461 | . 2 ⊢ (𝜑 → (𝜒 ∧ 𝜓)) |
| 3 | 2 | simpld 494 | 1 ⊢ (𝜑 → 𝜒) |
| Copyright terms: Public domain | W3C validator |