Theorem exp516

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

	Ref	Expression
Hypothesis	exp516.1	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) ∧ 𝜏 ) → 𝜂 )
Assertion	exp516	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp516.1	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) ∧ 𝜏 ) → 𝜂 )
2	1	exp31	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → ( 𝜏 → 𝜂 ) ) )
3	2	3expd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )