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Metamath Proof Explorer
Description: e21an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ee21an.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
|
ee21an.2 |
⊢ ( 𝜑 → 𝜃 ) |
|
|
ee21an.3 |
⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) |
|
Assertion |
ee21an |
⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ee21an.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
|
ee21an.2 |
⊢ ( 𝜑 → 𝜃 ) |
| 3 |
|
ee21an.3 |
⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) |
| 4 |
3
|
ex |
⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) ) |
| 5 |
1 2 4
|
syl6ci |
⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) ) |