Description: Closed form of a deduction based on com3r . Proposition 14 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege14 | ⊢ ( ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) → ( 𝜑 → ( 𝜃 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frege13 | ⊢ ( ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) → ( 𝜃 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) ) | |
| 2 | frege5 | ⊢ ( ( ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) → ( 𝜃 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) ) → ( ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) → ( 𝜑 → ( 𝜃 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) ) ) ) | |
| 3 | 1 2 | ax-mp | ⊢ ( ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) → ( 𝜑 → ( 𝜃 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) ) ) ) |