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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 1132 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒)) |
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