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  658  hbimd  1587  moim  2109  moimv  2111  sstr2  3191  ssralv  3248  soss  4350  nneneq  6919  prarloclem3  7566  fzind  9443  exbtwnzlemshrink  10340  rebtwn2zlemshrink  10345  seq3fveq2  10569  seqfveq2g  10571  seq3shft2  10575  seqshft2g  10576  monoord  10579  seq3split  10582  seqsplitg  10583  seq3id2  10620  seqhomog  10624  seq3coll  10936  rexico  11388  cnntr  14471  2sqlem6  15371  setindft  15621