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  658  hbimd  1584  moim  2106  moimv  2108  sstr2  3186  ssralv  3243  soss  4345  nneneq  6913  prarloclem3  7557  fzind  9432  exbtwnzlemshrink  10317  rebtwn2zlemshrink  10322  seq3fveq2  10546  seqfveq2g  10548  seq3shft2  10552  seqshft2g  10553  monoord  10556  seq3split  10559  seqsplitg  10560  seq3id2  10597  seqhomog  10601  seq3coll  10913  rexico  11365  cnntr  14393  2sqlem6  15207  setindft  15457