| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > adantr | Structured version Visualization version GIF version | ||
| Description: Inference adding a conjunct to the right of an antecedent. (Contributed by NM, 30-Aug-1993.) |
| Ref | Expression |
|---|---|
| adantr.1 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| adantr | ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | adantr.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | 1 | a1d 25 | . 2 ⊢ (𝜑 → (𝜒 → 𝜓)) |
| 3 | 2 | imp 406 | 1 ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
| Copyright terms: Public domain | W3C validator |