Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > com25 | Structured version Visualization version GIF version |
Description: Commutation of antecedents. Swap 2nd and 5th. Deduction associated with com14 94. (Contributed by Jeff Hankins, 28-Jun-2009.) |
Ref | Expression |
---|---|
com5.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Ref | Expression |
---|---|
com25 | ⊢ (𝜑 → (𝜏 → (𝜒 → (𝜃 → (𝜓 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com5.1 | . . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) | |
2 | 1 | com24 93 | . . 3 ⊢ (𝜑 → (𝜃 → (𝜒 → (𝜓 → (𝜏 → 𝜂))))) |
3 | 2 | com45 95 | . 2 ⊢ (𝜑 → (𝜃 → (𝜒 → (𝜏 → (𝜓 → 𝜂))))) |
4 | 3 | com24 93 | 1 ⊢ (𝜑 → (𝜏 → (𝜒 → (𝜃 → (𝜓 → 𝜂))))) |
Copyright terms: Public domain | W3C validator |