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| Mirrors > Home > MPE Home > Th. List > pm3.2i | Structured version Visualization version GIF version | ||
| Description: Infer conjunction of premises. Inference associated with pm3.2 469. Its associated deduction is jca 511 (and the double deduction is jcad 512). (Contributed by NM, 21-Jun-1993.) |
| Ref | Expression |
|---|---|
| pm3.2i.1 | ⊢ 𝜑 |
| pm3.2i.2 | ⊢ 𝜓 |
| Ref | Expression |
|---|---|
| pm3.2i | ⊢ (𝜑 ∧ 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm3.2i.1 | . 2 ⊢ 𝜑 | |
| 2 | pm3.2i.2 | . 2 ⊢ 𝜓 | |
| 3 | pm3.2 469 | . 2 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓))) | |
| 4 | 1, 2, 3 | mp2 9 | 1 ⊢ (𝜑 ∧ 𝜓) |
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