Theorem mpdi

Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005) (Proof shortened by Mel L. O'Cat, 15-Jan-2008)

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

Proof

Step	Hyp	Ref	Expression
1		mpdi.1	⊢ ( 𝜓 → 𝜒 )
2		mpdi.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	1	a1i	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	3 2	mpdd	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )