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Metamath Proof Explorer
Description: e112 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ee112.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
|
ee112.2 |
⊢ ( 𝜑 → 𝜒 ) |
|
|
ee112.3 |
⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) ) |
|
|
ee112.4 |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) ) |
|
Assertion |
ee112 |
⊢ ( 𝜑 → ( 𝜃 → 𝜂 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ee112.1 |
⊢ ( 𝜑 → 𝜓 ) |
| 2 |
|
ee112.2 |
⊢ ( 𝜑 → 𝜒 ) |
| 3 |
|
ee112.3 |
⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) ) |
| 4 |
|
ee112.4 |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) ) |
| 5 |
1
|
a1d |
⊢ ( 𝜑 → ( 𝜃 → 𝜓 ) ) |
| 6 |
2
|
a1d |
⊢ ( 𝜑 → ( 𝜃 → 𝜒 ) ) |
| 7 |
5 6 3 4
|
ee222 |
⊢ ( 𝜑 → ( 𝜃 → 𝜂 ) ) |