| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > simplll | Structured version Visualization version GIF version | ||
| Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009.) (Proof shortened by Wolf Lammen, 6-Apr-2022.) |
| Ref | Expression |
|---|---|
| simplll | ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ (𝜑 → 𝜑) | |
| 2 | 1 | ad3antrrr 730 | 1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑) |
| Copyright terms: Public domain | W3C validator |