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  663  hbimd  1621  moim  2144  moimv  2146  sstr2  3234  ssralv  3291  soss  4411  nneneq  7043  prarloclem3  7717  fzind  9595  exbtwnzlemshrink  10508  rebtwn2zlemshrink  10513  seq3fveq2  10737  seqfveq2g  10739  seq3shft2  10743  seqshft2g  10744  monoord  10747  seq3split  10750  seqsplitg  10751  seq3id2  10788  seqhomog  10792  seq3coll  11106  rexico  11782  cnntr  14951  2sqlem6  15851  setindft  16563