Metamath Proof Explorer
Description: A mixed syllogism inference from a nested implication and a
biconditional. (Contributed by NM, 21-Jun-1993)
|
|
Ref |
Expression |
|
Hypotheses |
imbitrdi.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
|
imbitrdi.2 |
⊢ ( 𝜒 ↔ 𝜃 ) |
|
Assertion |
imbitrdi |
⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
imbitrdi.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
2 |
|
imbitrdi.2 |
⊢ ( 𝜒 ↔ 𝜃 ) |
3 |
2
|
biimpi |
⊢ ( 𝜒 → 𝜃 ) |
4 |
1 3
|
syl6 |
⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) ) |