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  661  hbimd  1619  moim  2142  moimv  2144  sstr2  3232  ssralv  3289  soss  4409  nneneq  7038  prarloclem3  7710  fzind  9588  exbtwnzlemshrink  10501  rebtwn2zlemshrink  10506  seq3fveq2  10730  seqfveq2g  10732  seq3shft2  10736  seqshft2g  10737  monoord  10740  seq3split  10743  seqsplitg  10744  seq3id2  10781  seqhomog  10785  seq3coll  11099  rexico  11775  cnntr  14942  2sqlem6  15842  setindft  16510