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Metamath Proof Explorer
Description: Theorem *2.83 of WhiteheadRussell p. 108. Closed form of syld .
(Contributed by NM, 3-Jan-2005)
|
|
Ref |
Expression |
|
Assertion |
pm2.83 |
⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → ( 𝜒 → 𝜃 ) ) → ( 𝜑 → ( 𝜓 → 𝜃 ) ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
imim1 |
⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜒 → 𝜃 ) → ( 𝜓 → 𝜃 ) ) ) |
| 2 |
1
|
imim3i |
⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → ( 𝜒 → 𝜃 ) ) → ( 𝜑 → ( 𝜓 → 𝜃 ) ) ) ) |