Theorem mpdd 36

Description: A nested modus ponens deduction. (Contributed by NM, 12-Dec-2004.)

Hypotheses

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

Assertion

Ref	Expression
mpdd	|- ( ph -> ( ps -> th ) )

Proof of Theorem mpdd

Step	Hyp	Ref	Expression
1		mpdd.1	. 2 |- ( ph -> ( ps -> ch ) )
2		mpdd.2	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	a2d 23	. 2 |- ( ph -> ( ( ps -> ch ) -> ( ps -> th ) ) )
4	1, 3	mpd 13	1 |- ( ph -> ( ps -> th ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  mpid  37  mpdi  38  syld  40  syl6c  60  mpteqb  5261  oprabid  5537  nnmordi  6089  nnmord  6090  brecop  6196  findcard2  6346  findcard2s  6347  ordiso2  6357  zindd  8356  cau3lem  9710  climcau  9866