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	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
imim1d	⊢ (𝜑 → ((𝜒 → 𝜃) → (𝜓 → 𝜃)))

Proof of Theorem imim1d

Step	Hyp	Ref	Expression
1		imim1d.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		idd 21	. 2 ⊢ (𝜑 → (𝜃 → 𝜃))
3	1, 2	imim12d 74	1 ⊢ (𝜑 → ((𝜒 → 𝜃) → (𝜓 → 𝜃)))

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  2147  moimv  2149  sstr2  3249  ssralv  3306  soss  4440  nneneq  7124  prarloclem3  7828  fzind  9711  exbtwnzlemshrink  10632  rebtwn2zlemshrink  10637  seq3fveq2  10861  seqfveq2g  10863  seq3shft2  10867  seqshft2g  10868  monoord  10871  seq3split  10874  seqsplitg  10875  seq3id2  10912  seqhomog  10916  seq3coll  11239  rexico  11931  cnntr  15202  2sqlem6  16105  eupth2lemsfi  16585  setindft  16847