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Metamath Proof Explorer
Description: e012 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ee012.1 |
⊢ 𝜑 |
|
|
ee012.2 |
⊢ ( 𝜓 → 𝜒 ) |
|
|
ee012.3 |
⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) ) |
|
|
ee012.4 |
⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) ) |
|
Assertion |
ee012 |
⊢ ( 𝜓 → ( 𝜃 → 𝜂 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ee012.1 |
⊢ 𝜑 |
| 2 |
|
ee012.2 |
⊢ ( 𝜓 → 𝜒 ) |
| 3 |
|
ee012.3 |
⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) ) |
| 4 |
|
ee012.4 |
⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) ) |
| 5 |
1
|
a1i |
⊢ ( 𝜃 → 𝜑 ) |
| 6 |
5
|
a1i |
⊢ ( 𝜓 → ( 𝜃 → 𝜑 ) ) |
| 7 |
2
|
a1d |
⊢ ( 𝜓 → ( 𝜃 → 𝜒 ) ) |
| 8 |
6 7 3 4
|
ee222 |
⊢ ( 𝜓 → ( 𝜃 → 𝜂 ) ) |