Metamath Proof Explorer
Description: A mixed syllogism inference from a doubly nested implication and a
biconditional. (Contributed by NM, 14-May-1993)
|
|
Ref |
Expression |
|
Hypotheses |
syl7bi.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
|
|
syl7bi.2 |
⊢ ( 𝜒 → ( 𝜃 → ( 𝜓 → 𝜏 ) ) ) |
|
Assertion |
syl7bi |
⊢ ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
syl7bi.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
2 |
|
syl7bi.2 |
⊢ ( 𝜒 → ( 𝜃 → ( 𝜓 → 𝜏 ) ) ) |
3 |
1
|
biimpi |
⊢ ( 𝜑 → 𝜓 ) |
4 |
3 2
|
syl7 |
⊢ ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) |