Theorem exp42

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

	Ref	Expression
Hypothesis	exp42.1	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ∧ 𝜃 ) → 𝜏 )
Assertion	exp42	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		exp42.1	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ∧ 𝜃 ) → 𝜏 )
2	1	exp31	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → ( 𝜃 → 𝜏 ) ) )
3	2	expd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )