Description: Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 3imp1.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) | |
Assertion | 3imp1 | ⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imp1.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) | |
2 | 1 | 3imp | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜃 → 𝜏 ) ) |
3 | 2 | imp | ⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) |