Theorem expdimp

Description: A deduction version of exportation, followed by importation. (Contributed by NM, 6-Sep-2008)

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

Proof

Step	Hyp	Ref	Expression
1		expdimp.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
2	1	expd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )