Description: Closed form of jaoi . Proposition 50 of Frege1879 p. 49. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | frege50 | ⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜓 ) → ( ( ¬ 𝜑 → 𝜒 ) → 𝜓 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege49 | ⊢ ( ( ¬ 𝜑 → 𝜒 ) → ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜓 ) → 𝜓 ) ) ) | |
2 | frege17 | ⊢ ( ( ( ¬ 𝜑 → 𝜒 ) → ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜓 ) → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜓 ) → ( ( ¬ 𝜑 → 𝜒 ) → 𝜓 ) ) ) ) | |
3 | 1 2 | ax-mp | ⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜓 ) → ( ( ¬ 𝜑 → 𝜒 ) → 𝜓 ) ) ) |