Theorem expimpd

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

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

Proof

Step	Hyp	Ref	Expression
1		expimpd.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
2	1	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	impd	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )