Theorem 3impd

Description: Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006)

	Ref	Expression
Hypothesis	3imp1.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
Assertion	3impd	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		3imp1.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
2	1	com4l	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) )
3	2	3imp	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → ( 𝜑 → 𝜏 ) )
4	3	com12	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 ) )