Theorem imp45

Description: An importation inference. (Contributed by NM, 26-Apr-1994)

	Ref	Expression
Hypothesis	imp4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
Assertion	imp45	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		imp4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
2	1	imp4d	⊢ ( 𝜑 → ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 ) )
3	2	imp	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) → 𝜏 )