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| Mirrors > Home > MPE Home > Th. List > anasss | Structured version Visualization version GIF version | ||
| Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by NM, 15-Nov-2002.) |
| Ref | Expression |
|---|---|
| anasss.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| anasss | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anasss.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
| 2 | 1 | exp31 419 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| 3 | 2 | imp32 418 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
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