Theorem exp5o

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

	Ref	Expression
Hypothesis	exp5o.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) )
Assertion	exp5o	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp5o.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) )
2	1	expd	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
3	2	3exp	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )