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 ) ) )

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:  imim1  76  imbi1d  231  expt  667  hbimd  1626  moim  2151  moimv  2153  sstr2  3255  ssralv  3312  soss  4461  nneneq  7164  prarloclem3  7870  fzind  9771  exbtwnzlemshrink  10699  rebtwn2zlemshrink  10704  seq3fveq2  10932  seqfveq2g  10934  seq3shft2  10938  seqshft2g  10939  monoord  10942  seq3split  10945  seqsplitg  10946  seq3id2  10983  seqhomog  10987  seq3coll  11315  rexico  12009  cnntr  15468  bcmono  16321  2sqlem6  16461  eupth2lemsfi  16941  setindft  17213