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Metamath Proof Explorer
Description: A syllogism rule of inference. The second premise is used to replace
the consequent of the first premise. (Contributed by NM, 1-Aug-1994)
|
|
Ref |
Expression |
|
Hypotheses |
syl8ib.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
|
|
syl8ib.2 |
⊢ ( 𝜃 ↔ 𝜏 ) |
|
Assertion |
syl8ib |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
syl8ib.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
| 2 |
|
syl8ib.2 |
⊢ ( 𝜃 ↔ 𝜏 ) |
| 3 |
2
|
biimpi |
⊢ ( 𝜃 → 𝜏 ) |
| 4 |
1 3
|
syl8 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) |