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Metamath Proof Explorer
Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994) (Proof shortened by Mel L. O'Cat, 15-Aug-2004)
|
|
Ref |
Expression |
|
Hypothesis |
com4.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) |
|
Assertion |
com4l |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
com4.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) |
| 2 |
1
|
com3l |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → ( 𝜃 → 𝜏 ) ) ) ) |
| 3 |
2
|
com34 |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) ) |