Metamath Proof Explorer
Description: A syllogism inference combined with contraction. (Contributed by Alan
Sare, 18-Mar-2012)
|
|
Ref |
Expression |
|
Hypotheses |
syl6ci.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
|
syl6ci.2 |
⊢ ( 𝜑 → 𝜃 ) |
|
|
syl6ci.3 |
⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) ) |
|
Assertion |
syl6ci |
⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
syl6ci.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
2 |
|
syl6ci.2 |
⊢ ( 𝜑 → 𝜃 ) |
3 |
|
syl6ci.3 |
⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) ) |
4 |
2
|
a1d |
⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) ) |
5 |
1 4 3
|
syl6c |
⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) ) |