Theorem mpii

Description: A doubly nested modus ponens inference. (Contributed by NM, 31-Dec-1993) (Proof shortened by Wolf Lammen, 31-Jul-2012)

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

Proof

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