Theorem a2i

Description: Inference distributing an antecedent. Inference associated with ax-2 . Its associated inference is mpd . (Contributed by NM, 29-Dec-1992)

	Ref	Expression
Hypothesis	a2i.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	a2i	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		a2i.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ax-2	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) )