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	|- ch
	mpii.2	|- ( ph -> ( ps -> ( ch -> th ) ) )
Assertion	mpii	|- ( ph -> ( ps -> th ) )

Proof

Step	Hyp	Ref	Expression
1		mpii.1	|- ch
2		mpii.2	|- ( ph -> ( ps -> ( ch -> th ) ) )
3	1	a1i	|- ( ps -> ch )
4	3 2	mpdi	|- ( ph -> ( ps -> th ) )