Description: Closed form of syl5 . Derived automatically from syl5impVD . (Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | syl5imp | ⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜃 → 𝜓 ) → ( 𝜑 → ( 𝜃 → 𝜒 ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm2.04 | ⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) ) | |
| 2 | 1 | imim2d | ⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → ( 𝜑 → 𝜒 ) ) ) ) |
| 3 | 2 | com34 | ⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜃 → 𝜓 ) → ( 𝜑 → ( 𝜃 → 𝜒 ) ) ) ) |