Theorem 3exp

Description: Exportation inference. (Contributed by NM, 30-May-1994) (Proof shortened by Wolf Lammen, 22-Jun-2022)

	Ref	Expression
Hypothesis	3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	3exp	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3expa	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
3	2	exp31	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )