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  661  hbimd  1619  moim  2142  moimv  2144  sstr2  3231  ssralv  3288  soss  4405  nneneq  7018  prarloclem3  7684  fzind  9562  exbtwnzlemshrink  10468  rebtwn2zlemshrink  10473  seq3fveq2  10697  seqfveq2g  10699  seq3shft2  10703  seqshft2g  10704  monoord  10707  seq3split  10710  seqsplitg  10711  seq3id2  10748  seqhomog  10752  seq3coll  11064  rexico  11732  cnntr  14899  2sqlem6  15799  setindft  16328