Description: An importation inference. (Contributed by NM, 26-Apr-1994)
Ref | Expression | ||
---|---|---|---|
Hypothesis | imp4.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) | |
Assertion | imp4d | ⊢ ( 𝜑 → ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp4.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) | |
2 | 1 | imp4a | ⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) ) |
3 | 2 | impd | ⊢ ( 𝜑 → ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 ) ) |