Metamath Proof Explorer
Description: e100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
ee100.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
|
ee100.2 |
⊢ 𝜒 |
|
|
ee100.3 |
⊢ 𝜃 |
|
|
ee100.4 |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) |
|
Assertion |
ee100 |
⊢ ( 𝜑 → 𝜏 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ee100.1 |
⊢ ( 𝜑 → 𝜓 ) |
2 |
|
ee100.2 |
⊢ 𝜒 |
3 |
|
ee100.3 |
⊢ 𝜃 |
4 |
|
ee100.4 |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) |
5 |
2
|
a1i |
⊢ ( 𝜑 → 𝜒 ) |
6 |
3
|
a1i |
⊢ ( 𝜑 → 𝜃 ) |
7 |
1 5 6 4
|
syl3c |
⊢ ( 𝜑 → 𝜏 ) |