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| Mirrors > Home > MPE Home > Th. List > mp1i | Structured version Visualization version GIF version | ||
| Description: Inference detaching an antecedent and introducing a new one. (Contributed by Stefan O'Rear, 29-Jan-2015.) |
| Ref | Expression |
|---|---|
| mp1i.1 | ⊢ 𝜑 |
| mp1i.2 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| mp1i | ⊢ (𝜒 → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mp1i.1 | . . 3 ⊢ 𝜑 | |
| 2 | mp1i.2 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 3 | 1, 2 | ax-mp 5 | . 2 ⊢ 𝜓 |
| 4 | 3 | a1i 11 | 1 ⊢ (𝜒 → 𝜓) |
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