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| Mirrors > Home > MPE Home > Th. List > com23 | Structured version Visualization version GIF version | ||
| Description: Commutation of antecedents. Swap 2nd and 3rd. Deduction associated with com12 32. (Contributed by NM, 27-Dec-1992.) (Proof shortened by Wolf Lammen, 4-Aug-2012.) |
| Ref | Expression |
|---|---|
| com3.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| Ref | Expression |
|---|---|
| com23 | ⊢ (𝜑 → (𝜒 → (𝜓 → 𝜃))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | com3.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
| 2 | pm2.27 42 | . 2 ⊢ (𝜒 → ((𝜒 → 𝜃) → 𝜃)) | |
| 3 | 1, 2 | syl9 77 | 1 ⊢ (𝜑 → (𝜒 → (𝜓 → 𝜃))) |
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