Metamath Proof Explorer
Description: e30 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ee30.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
|
|
ee30.2 |
⊢ 𝜏 |
|
|
ee30.3 |
⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) ) |
|
Assertion |
ee30 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ee30.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
2 |
|
ee30.2 |
⊢ 𝜏 |
3 |
|
ee30.3 |
⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) ) |
4 |
2
|
a1i |
⊢ ( 𝜒 → 𝜏 ) |
5 |
4
|
a1i |
⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) ) |
6 |
5
|
a1i |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) |
7 |
1 6 3
|
ee33 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) ) |