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| Mirrors > Home > MPE Home > Th. List > 3adant1r | Structured version Visualization version GIF version | ||
| Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) |
| Ref | Expression |
|---|---|
| ad4ant3.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| 3adant1r | ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜓 ∧ 𝜒) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpl 482 | . 2 ⊢ ((𝜑 ∧ 𝜏) → 𝜑) | |
| 2 | ad4ant3.1 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
| 3 | 1, 2 | syl3an1 1164 | 1 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜓 ∧ 𝜒) → 𝜃) |
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