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  5393  oprabid  5681  nnmordi  6275  nnmord  6276  brecop  6382  findcard2  6605  findcard2s  6606  ordiso2  6728  zindd  8864  cau3lem  10547  climcau  10736  dvdsabseq  11126