Metamath Proof Explorer
Description: A mixed syllogism inference. In the process of being renamed to
biimtrdi . (Contributed by NM, 2-Jan-1994)
|
|
Ref |
Expression |
|
Hypotheses |
syl6bi.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
|
|
syl6bi.2 |
⊢ ( 𝜒 → 𝜃 ) |
|
Assertion |
syl6bi |
⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
syl6bi.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
2 |
|
syl6bi.2 |
⊢ ( 𝜒 → 𝜃 ) |
3 |
1
|
biimpd |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
4 |
3 2
|
syl6 |
⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) ) |