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  1622  moim  2144  moimv  2146  sstr2  3235  ssralv  3292  soss  4417  nneneq  7086  prarloclem3  7777  fzind  9656  exbtwnzlemshrink  10571  rebtwn2zlemshrink  10576  seq3fveq2  10800  seqfveq2g  10802  seq3shft2  10806  seqshft2g  10807  monoord  10810  seq3split  10813  seqsplitg  10814  seq3id2  10851  seqhomog  10855  seq3coll  11169  rexico  11861  cnntr  15036  2sqlem6  15939  eupth2lemsfi  16419  setindft  16681