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| Mirrors > Home > MPE Home > Th. List > adantllr | Structured version Visualization version GIF version | ||
| Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.) |
| Ref | Expression |
|---|---|
| adantl2.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| adantllr | ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpl 482 | . 2 ⊢ ((𝜑 ∧ 𝜏) → 𝜑) | |
| 2 | adantl2.1 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
| 3 | 1, 2 | sylanl1 680 | 1 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃) |
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