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| Mirrors > Home > MPE Home > Th. List > simpld | Structured version Visualization version GIF version | ||
| Description: Deduction eliminating a conjunct. A translation of natural deduction rule ∧ EL (∧ elimination left), see natded 30422. (Contributed by NM, 26-May-1993.) |
| Ref | Expression |
|---|---|
| simpld.1 | ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
| Ref | Expression |
|---|---|
| simpld | ⊢ (𝜑 → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpld.1 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) | |
| 2 | simpl 482 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜓) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝜓) |
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