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| Mirrors > Home > MPE Home > Th. List > ancoms | Structured version Visualization version GIF version | ||
| Description: Inference commuting conjunction in antecedent. (Contributed by NM, 21-Apr-1994.) |
| Ref | Expression |
|---|---|
| ancoms.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Ref | Expression |
|---|---|
| ancoms | ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ancoms.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 2 | 1 | expcom 413 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) |
| 3 | 2 | imp 406 | 1 ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
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