Description: Special case of closed form of a2d . Special case of rp-frege4g . Proposition 4 of Frege1879 p. 31. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege4 | ⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frege3 | ⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → ( 𝜑 → 𝜓 ) ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) ) ) | |
| 2 | ax-frege2 | ⊢ ( ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → ( 𝜑 → 𝜓 ) ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) ) ) → ( ( ( 𝜑 → 𝜓 ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) ) ) ) | |
| 3 | 1 2 | ax-mp | ⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) ) ) |