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| Mirrors > Home > MPE Home > Th. List > simpll1 | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) |
| Ref | Expression |
|---|---|
| simpll1 | ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simp1 1137 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑) | |
| 2 | 1 | ad2antrr 726 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑) |
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