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| Mirrors > Home > MPE Home > Th. List > adantl | Structured version Visualization version GIF version | ||
| Description: Inference adding a conjunct to the left of an antecedent. (Contributed by NM, 30-Aug-1993.) (Proof shortened by Wolf Lammen, 23-Nov-2012.) |
| Ref | Expression |
|---|---|
| adantl.1 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| adantl | ⊢ ((𝜒 ∧ 𝜑) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | adantl.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | 1 | adantr 480 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
| 3 | 2 | ancoms 458 | 1 ⊢ ((𝜒 ∧ 𝜑) → 𝜓) |
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