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-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  mp2d  47  pm2.43a  51  embantd  56  mpan2d  428  ceqsalt  2829  rspcimdv  2911  fvimacnv  5762  riotass2  6000  pr2ne  7397  0mnnnnn0  9434  caucvgre  11546  climcn1  11873  climcn2  11874  gcdaddm  12560  dvdsgcd  12588  coprmgcdb  12665  nprm  12700  pcqmul  12881  grpid  13627  uniopn  14731  metcnp3  15241  cncfco  15321  eupth2fi  16336