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| Mirrors > Home > MPE Home > Th. List > 3pm3.2i | Structured version Visualization version GIF version | ||
| Description: Infer conjunction of premises. (Contributed by NM, 10-Feb-1995.) |
| Ref | Expression |
|---|---|
| 3pm3.2i.1 | ⊢ 𝜑 |
| 3pm3.2i.2 | ⊢ 𝜓 |
| 3pm3.2i.3 | ⊢ 𝜒 |
| Ref | Expression |
|---|---|
| 3pm3.2i | ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3pm3.2i.1 | . . 3 ⊢ 𝜑 | |
| 2 | 3pm3.2i.2 | . . 3 ⊢ 𝜓 | |
| 3 | 1, 2 | pm3.2i 470 | . 2 ⊢ (𝜑 ∧ 𝜓) |
| 4 | 3pm3.2i.3 | . 2 ⊢ 𝜒 | |
| 5 | df-3an 1089 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒)) | |
| 6 | 3, 4, 5 | mpbir2an 711 | 1 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒) |
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