This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009)
(Proof shortened by Wolf Lammen, 2-Aug-2022)
|
|
Ref |
Expression |
|
Hypothesis |
imp5.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |
|
Assertion |
imp5a |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
imp5.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |
| 2 |
1
|
imp5d |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) ) |
| 3 |
2
|
exp31 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) ) ) ) |