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 ) ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  imim1  76  imbi1d  231  expt  667  hbimd  1626  moim  2151  moimv  2153  sstr2  3255  ssralv  3312  soss  4459  nneneq  7158  prarloclem3  7864  fzind  9761  exbtwnzlemshrink  10683  rebtwn2zlemshrink  10688  seq3fveq2  10912  seqfveq2g  10914  seq3shft2  10918  seqshft2g  10919  monoord  10922  seq3split  10925  seqsplitg  10926  seq3id2  10963  seqhomog  10967  seq3coll  11294  rexico  11987  cnntr  15326  2sqlem6  16239  eupth2lemsfi  16719  setindft  16991