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

Proof

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