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Metamath Proof Explorer
Description: Commutation of antecedents. Swap 1st and 5th. (Contributed by Jeff
Hankins, 28-Jun-2009) (Proof shortened by Wolf Lammen, 29-Jul-2012)
|
|
Ref |
Expression |
|
Hypothesis |
com5.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |
|
Assertion |
com15 |
⊢ ( 𝜏 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜂 ) ) ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
com5.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |
| 2 |
1
|
com5l |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → ( 𝜑 → 𝜂 ) ) ) ) ) |
| 3 |
2
|
com4r |
⊢ ( 𝜏 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜂 ) ) ) ) ) |