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| Mirrors > Home > MPE Home > Th. List > simp3bi | Structured version Visualization version GIF version | ||
| Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
| Ref | Expression |
|---|---|
| 3simp1bi.1 | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃)) |
| Ref | Expression |
|---|---|
| simp3bi | ⊢ (𝜑 → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3simp1bi.1 | . . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃)) | |
| 2 | 1 | biimpi 216 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃)) |
| 3 | 2 | simp3d 1145 | 1 ⊢ (𝜑 → 𝜃) |
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