Theorem exp53

Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009)

	Ref	Expression
Hypothesis	exp53.1	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ∧ 𝜏 ) → 𝜂 )
Assertion	exp53	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp53.1	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ∧ 𝜏 ) → 𝜂 )
2	1	ex	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) → ( 𝜏 → 𝜂 ) )
3	2	exp43	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )