Theorem impd

Description: Importation deduction. (Contributed by NM, 31-Mar-1994)

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

Proof

Step	Hyp	Ref	Expression
1		impd.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2	1	com3l	⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜃 ) ) )
3	2	imp	⊢ ( ( 𝜓 ∧ 𝜒 ) → ( 𝜑 → 𝜃 ) )
4	3	com12	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )