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| Mirrors > Home > MPE Home > Th. List > com24 | Structured version Visualization version GIF version | ||
| Description: Commutation of antecedents. Swap 2nd and 4th. Deduction associated with com13 88. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.) |
| Ref | Expression |
|---|---|
| com4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
| Ref | Expression |
|---|---|
| com24 | ⊢ (𝜑 → (𝜃 → (𝜒 → (𝜓 → 𝜏)))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | com4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
| 2 | 1 | com4t 93 | . 2 ⊢ (𝜒 → (𝜃 → (𝜑 → (𝜓 → 𝜏)))) |
| 3 | 2 | com13 88 | 1 ⊢ (𝜑 → (𝜃 → (𝜒 → (𝜓 → 𝜏)))) |
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