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| Mirrors > Home > MPE Home > Th. List > 3impa | Structured version Visualization version GIF version | ||
| Description: Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.) (Revised to shorten 3imp 1111 by Wolf Lammen, 20-Jun-2022.) |
| Ref | Expression |
|---|---|
| 3impa.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| 3impa | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-3an 1089 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒)) | |
| 2 | 3impa.1 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
| 3 | 1, 2 | sylbi 217 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
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