Theorem imim1d 75

Description: Deduction adding nested consequents. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)

Hypothesis

Ref	Expression
imim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
imim1d	|- ( ph -> ( ( ch -> th ) -> ( ps -> th ) ) )

Proof of Theorem imim1d

Step	Hyp	Ref	Expression
1		imim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
2		idd 21	. 2 |- ( ph -> ( th -> th ) )
3	1, 2	imim12d 74	1 |- ( ph -> ( ( ch -> th ) -> ( 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:  imim1  76  imbi1d  231  expt  657  hbimd  1573  moim  2090  moimv  2092  sstr2  3164  ssralv  3221  soss  4316  nneneq  6859  prarloclem3  7498  fzind  9370  exbtwnzlemshrink  10251  rebtwn2zlemshrink  10256  seq3fveq2  10471  seq3shft2  10475  monoord  10478  seq3split  10481  seq3id2  10511  seq3coll  10824  rexico  11232  cnntr  13764  2sqlem6  14506  setindft  14756