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  1584  moim  2106  moimv  2108  sstr2  3187  ssralv  3244  soss  4346  nneneq  6915  prarloclem3  7559  fzind  9435  exbtwnzlemshrink  10320  rebtwn2zlemshrink  10325  seq3fveq2  10549  seqfveq2g  10551  seq3shft2  10555  seqshft2g  10556  monoord  10559  seq3split  10562  seqsplitg  10563  seq3id2  10600  seqhomog  10604  seq3coll  10916  rexico  11368  cnntr  14404  2sqlem6  15277  setindft  15527