Metamath Proof Explorer
Description: e211 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ee211.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
|
ee211.2 |
⊢ ( 𝜑 → 𝜃 ) |
|
|
ee211.3 |
⊢ ( 𝜑 → 𝜏 ) |
|
|
ee211.4 |
⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) |
|
Assertion |
ee211 |
⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ee211.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
2 |
|
ee211.2 |
⊢ ( 𝜑 → 𝜃 ) |
3 |
|
ee211.3 |
⊢ ( 𝜑 → 𝜏 ) |
4 |
|
ee211.4 |
⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) |
5 |
2
|
a1d |
⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) ) |
6 |
3
|
a1d |
⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) ) |
7 |
1 5 6 4
|
ee222 |
⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) ) |