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| Mirrors > Home > MPE Home > Th. List > simpl1 | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) |
| Ref | Expression |
|---|---|
| simpl1 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpl 482 | . 2 ⊢ ((𝜑 ∧ 𝜃) → 𝜑) | |
| 2 | 1 | 3ad2antl1 1186 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑) |
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