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Metamath Proof Explorer
Description: Conjunction form of ee30 . (Contributed by Alan Sare, 17-Jul-2011)
(Proof modification is discouraged.) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ee30an.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
|
|
ee30an.2 |
⊢ 𝜏 |
|
|
ee30an.3 |
⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) |
|
Assertion |
ee30an |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ee30an.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
| 2 |
|
ee30an.2 |
⊢ 𝜏 |
| 3 |
|
ee30an.3 |
⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) |
| 4 |
3
|
ex |
⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) ) |
| 5 |
1 2 4
|
ee30 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) ) |