Theorem imp5p

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

	Ref	Expression
Hypothesis	3imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
Assertion	imp5p	⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		3imp5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
2	1	com52l	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → ( 𝜑 → ( 𝜓 → 𝜂 ) ) ) ) )
3	2	3imp	⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) → ( 𝜑 → ( 𝜓 → 𝜂 ) ) )
4	3	com3l	⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜂 ) ) )