Theorem imp5a

Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009) (Proof shortened by Wolf Lammen, 2-Aug-2022)

	Ref	Expression
Hypothesis	imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
Assertion	imp5a	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
2	1	imp5d	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) )
3	2	exp31	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) ) ) )