| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > ad4ant14 | Structured version Visualization version GIF version | ||
| Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.) |
| Ref | Expression |
|---|---|
| ad4ant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Ref | Expression |
|---|---|
| ad4ant14 | ⊢ ((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ad4ant2.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 2 | 1 | adantlr 715 | . 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒) |
| 3 | 2 | adantlr 715 | 1 ⊢ ((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) → 𝜒) |
| Copyright terms: Public domain | W3C validator |