Theorem mpdd 40

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-1 5  ax-2 6  ax-mp 7

This theorem is referenced by:  mpid  41  mpdi  42  syld  44  syl6c  65  mpteqb  5293  oprabid  5568  nnmordi  6155  nnmord  6156  brecop  6262  findcard2  6423  findcard2s  6424  ordiso2  6505  zindd  8546  cau3lem  10138  climcau  10322  dvdsabseq  10392