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Mirrors > Home > MPE Home > Th. List > 3simpa | Structured version Visualization version GIF version |
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) |
Ref | Expression |
---|---|
3simpa | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜑 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 1033 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒)) | |
2 | 1 | simplbi 475 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜑 ∧ 𝜓)) |
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