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| Mirrors > Home > MPE Home > Th. List > an32s | Structured version Visualization version GIF version | ||
| Description: Swap two conjuncts in antecedent. (Contributed by NM, 13-Mar-1996.) |
| Ref | Expression |
|---|---|
| an32s.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| an32s | ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | an32 646 | . 2 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒)) | |
| 2 | an32s.1 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
| 3 | 1, 2 | sylbi 217 | 1 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃) |
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