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  667  hbimd  1626  moim  2151  moimv  2153  sstr2  3255  ssralv  3312  soss  4457  nneneq  7151  prarloclem3  7857  fzind  9743  exbtwnzlemshrink  10664  rebtwn2zlemshrink  10669  seq3fveq2  10893  seqfveq2g  10895  seq3shft2  10899  seqshft2g  10900  monoord  10903  seq3split  10906  seqsplitg  10907  seq3id2  10944  seqhomog  10948  seq3coll  11275  rexico  11968  cnntr  15252  2sqlem6  16156  eupth2lemsfi  16636  setindft  16908