Theorem mpid

Description: A nested modus ponens deduction. Deduction associated with mpi . (Contributed by NM, 14-Dec-2004)

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

Proof

Step	Hyp	Ref	Expression
1		mpid.1	⊢ ( 𝜑 → 𝜒 )
2		mpid.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	1	a1d	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	3 2	mpdd	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )