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| Mirrors > Home > MPE Home > Th. List > 3simpc | Structured version Visualization version GIF version | ||
| Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 21-Jun-2022.) |
| Ref | Expression |
|---|---|
| 3simpc | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ ((𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒)) | |
| 2 | 1 | 3adant1 1131 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒)) |
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