Theorem imp55

Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009)

	Ref	Expression
Hypothesis	imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
Assertion	imp55	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) ∧ 𝜏 ) → 𝜂 )

Proof

Step	Hyp	Ref	Expression
1		imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
2	1	imp4a	⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → ( 𝜏 → 𝜂 ) ) ) )
3	2	imp42	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) ∧ 𝜏 ) → 𝜂 )