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| Mirrors > Home > MPE Home > Th. List > simplbi | Structured version Visualization version GIF version | ||
| Description: Deduction eliminating a conjunct. (Contributed by NM, 27-May-1998.) |
| Ref | Expression |
|---|---|
| simplbi.1 | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) |
| Ref | Expression |
|---|---|
| simplbi | ⊢ (𝜑 → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simplbi.1 | . . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) | |
| 2 | 1 | biimpi 216 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
| 3 | 2 | simpld 494 | 1 ⊢ (𝜑 → 𝜓) |
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