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| Mirrors > Home > MPE Home > Th. List > com34 | Structured version Visualization version GIF version | ||
| Description: Commutation of antecedents. Swap 3rd and 4th. Deduction associated with com23 86. Double deduction associated with com12 32. (Contributed by NM, 25-Apr-1994.) |
| Ref | Expression |
|---|---|
| com4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
| Ref | Expression |
|---|---|
| com34 | ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏)))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | com4.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
| 2 | pm2.04 90 | . 2 ⊢ ((𝜒 → (𝜃 → 𝜏)) → (𝜃 → (𝜒 → 𝜏))) | |
| 3 | 1, 2 | syl6 35 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏)))) |
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