Theorem exp44

Description: An exportation inference. (Contributed by NM, 26-Apr-1994)

	Ref	Expression
Hypothesis	exp44.1	⊢ ( ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) → 𝜏 )
Assertion	exp44	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp44.1	⊢ ( ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) → 𝜏 )
2	1	exp32	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → ( 𝜃 → 𝜏 ) ) )
3	2	expd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )