Theorem imp5q

Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009)

	Ref	Expression
Hypothesis	3imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
Assertion	imp5q	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜂 ) )

Proof

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