Theorem mpid 42

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 41	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  47  pm2.43a  51  embantd  56  mpan2d  422  ceqsalt  2667  rspcimdv  2745  fvimacnv  5467  riotass2  5688  pr2ne  6959  0mnnnnn0  8861  caucvgre  10593  climcn1  10916  climcn2  10917  gcdaddm  11467  dvdsgcd  11493  coprmgcdb  11562  nprm  11597  uniopn  11950  metcnp3  12435  cncfco  12491