Theorem imim3i

Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006)

	Ref	Expression
Hypothesis	imim3i.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	imim3i	⊢ ( ( 𝜃 → 𝜑 ) → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim3i.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	imim2i	⊢ ( ( 𝜃 → 𝜑 ) → ( 𝜃 → ( 𝜓 → 𝜒 ) ) )
3	2	a2d	⊢ ( ( 𝜃 → 𝜑 ) → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) )