Theorem imp

Description: Importation inference. (Contributed by NM, 3-Jan-1993) (Proof shortened by Eric Schmidt, 22-Dec-2006)

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

Proof

Step	Hyp	Ref	Expression
1		imp.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		df-an	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 → ¬ 𝜓 ) )
3	1	impi	⊢ ( ¬ ( 𝜑 → ¬ 𝜓 ) → 𝜒 )
4	2 3	sylbi	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )