Theorem imp5d

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

	Ref	Expression
Hypothesis	imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
Assertion	imp5d	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
2	1	imp31	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
3	2	impd	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) )