Theorem mp2d 41

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

Hypotheses

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

Assertion

Ref	Expression
mp2d	|- (ph -> th)

Proof of Theorem mp2d

Step	Hyp	Ref	Expression
1		mp2d.1	. 2 |- (ph -> ps)
2		mp2d.2	. . 3 |- (ph -> ch)
3		mp2d.3	. . 3 |- (ph -> (ps -> (ch -> th)))
4	2, 3	mpid 37	. 2 |- (ph -> (ps -> th))
5	1, 4	mpd 14	1 |- (ph -> th)

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by: (None)