This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)
|
|
Ref |
Expression |
|
Hypothesis |
com3.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
|
Assertion |
com3l |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
com3.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
| 2 |
1
|
com3r |
⊢ ( 𝜒 → ( 𝜑 → ( 𝜓 → 𝜃 ) ) ) |
| 3 |
2
|
com3r |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) |