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 410 | 1 ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
Copyright terms: Public domain | W3C validator |