Metamath Proof Explorer
Description: Commutation of antecedents. Swap 1st and 4th. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)
|
|
Ref |
Expression |
|
Hypothesis |
com4.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) |
|
Assertion |
com14 |
⊢ ( 𝜃 → ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜏 ) ) ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
com4.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) |
2 |
1
|
com4l |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) ) |
3 |
2
|
com3r |
⊢ ( 𝜃 → ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜏 ) ) ) ) |