Theorem mpdd 41

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 26	. 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-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  mpid  42  mpdi  43  syld  45  syl6c  66  mpteqb  5693  oprabid  5999  nnmordi  6625  nnmord  6626  brecop  6735  findcard2  7012  findcard2s  7013  ordiso2  7163  zindd  9526  ccatopth2  11208  cau3lem  11540  climcau  11773  dvdsabseq  12273  znrrg  14537  metrest  15093  bj-charfunr  15945