Theorem mpdd

Description: A nested modus ponens deduction. Double deduction associated with ax-mp . Deduction associated with mpd . (Contributed by NM, 12-Dec-2004)

	Ref	Expression
Hypotheses	mpdd.1	|- ( ph -> ( ps -> ch ) )
	mpdd.2	|- ( ph -> ( ps -> ( ch -> th ) ) )
Assertion	mpdd	|- ( ph -> ( ps -> th ) )

Proof

Step	Hyp	Ref	Expression
1		mpdd.1	|- ( ph -> ( ps -> ch ) )
2		mpdd.2	|- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	a2d	|- ( ph -> ( ( ps -> ch ) -> ( ps -> th ) ) )
4	1 3	mpd	|- ( ph -> ( ps -> th ) )