Theorem mpid 37

Description: A nested modus ponens deduction. (Contributed by NM, 14-Dec-2004.)

Hypotheses

Ref	Expression
mpid.1	|- ( ph -> ch )
mpid.2	|- ( ph -> ( ps -> ( ch -> th ) ) )

Assertion

Ref	Expression
mpid	|- ( ph -> ( ps -> th ) )

Proof of Theorem mpid

Step	Hyp	Ref	Expression
1		mpid.1	. . 3 |- ( ph -> ch )
2	1	a1d 22	. 2 |- ( ph -> ( ps -> ch ) )
3		mpid.2	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
4	2, 3	mpdd 36	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:  mp2d  41  pm2.43a  45  embantd  50  mpan2d  404  ceqsalt  2580  rspcimdv  2657  fvimacnv  5282  riotass2  5494  0mnnnnn0  8214  caucvgre  9580  climcn1  9829  climcn2  9830