Theorem mpd

Description: A modus ponens deduction. A translation of natural deduction rule -> E ( -> elimination), see natded . Deduction form of ax-mp . Inference associated with a2i . Commuted form of mpcom . (Contributed by NM, 29-Dec-1992)

	Ref	Expression
Hypotheses	mpd.1	⊢ ( 𝜑 → 𝜓 )
	mpd.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	mpd	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		mpd.1	⊢ ( 𝜑 → 𝜓 )
2		mpd.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	a2i	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) )
4	1 3	ax-mp	⊢ ( 𝜑 → 𝜒 )