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  5649  oprabid  5951  nnmordi  6571  nnmord  6572  brecop  6681  findcard2  6947  findcard2s  6948  ordiso2  7096  zindd  9438  cau3lem  11261  climcau  11493  dvdsabseq  11992  znrrg  14159  metrest  14685  bj-charfunr  15372