Description: Replacement of a nested antecedent with an outer antecedent. Commuted simplificated form of elimination of a nested antecedent. Also holds intuitionistically. Polish prefix notation: CCCpqrCsCqr . (Contributed by ADH, 10-Nov-2023) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | adh-jarrsc | ⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜃 → ( 𝜓 → 𝜒 ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jarr | ⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) | |
| 2 | ax-1 | ⊢ ( ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) → ( 𝜃 → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) ) ) | |
| 3 | 1 2 | ax-mp | ⊢ ( 𝜃 → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) ) |
| 4 | pm2.04 | ⊢ ( ( 𝜃 → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜃 → ( 𝜓 → 𝜒 ) ) ) ) | |
| 5 | 3 4 | ax-mp | ⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜃 → ( 𝜓 → 𝜒 ) ) ) |