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| Mirrors > Home > MPE Home > Th. List > 3adantl3 | Structured version Visualization version GIF version | ||
| Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.) |
| Ref | Expression |
|---|---|
| 3adantl.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| 3adantl3 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3simpa 1149 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜏) → (𝜑 ∧ 𝜓)) | |
| 2 | 3adantl.1 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
| 3 | 1, 2 | sylan 580 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
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