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| Mirrors > Home > MPE Home > Th. List > simp1d | Structured version Visualization version GIF version | ||
| Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.) |
| Ref | Expression |
|---|---|
| 3simp1d.1 | ⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃)) |
| Ref | Expression |
|---|---|
| simp1d | ⊢ (𝜑 → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3simp1d.1 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃)) | |
| 2 | simp1 1137 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜓) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝜓) |
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