Theorem mp2d

Description: A double modus ponens deduction. Deduction associated with mp2 . (Contributed by NM, 23-May-2013) (Proof shortened by Wolf Lammen, 23-Jul-2013)

	Ref	Expression
Hypotheses	mp2d.1	|- ( ph -> ps )
	mp2d.2	|- ( ph -> ch )
	mp2d.3	|- ( ph -> ( ps -> ( ch -> th ) ) )
Assertion	mp2d	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		mp2d.1	|- ( ph -> ps )
2		mp2d.2	|- ( ph -> ch )
3		mp2d.3	|- ( ph -> ( ps -> ( ch -> th ) ) )
4	2 3	mpid	|- ( ph -> ( ps -> th ) )
5	1 4	mpd	|- ( ph -> th )