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 ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  mp2d  47  pm2.43a  51  embantd  56  mpan2d  432  ceqsalt  2848  rspcimdv  2930  fvimacnv  5824  riotass2  6067  pr2ne  7538  0mnnnnn0  9595  caucvgre  11747  climcn1  12074  climcn2  12075  gcdaddm  12761  dvdsgcd  12789  coprmgcdb  12866  nprm  12901  pcqmul  13082  grpid  13844  uniopn  15102  metcnp3  15612  cncfco  15692  eupth2fi  16720