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  5790  oprabid  6107  nnmordi  6779  nnmord  6780  brecop  6889  findcard2  7183  findcard2s  7184  ordiso2  7365  zindd  9743  ccatopth2  11467  cau3lem  11858  climcau  12091  dvdsabseq  12592  znrrg  14967  metrest  15530  bj-charfunr  16750