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  1621  moim  2144  moimv  2146  sstr2  3234  ssralv  3291  soss  4411  nneneq  7043  prarloclem3  7717  fzind  9595  exbtwnzlemshrink  10509  rebtwn2zlemshrink  10514  seq3fveq2  10738  seqfveq2g  10740  seq3shft2  10744  seqshft2g  10745  monoord  10748  seq3split  10751  seqsplitg  10752  seq3id2  10789  seqhomog  10793  seq3coll  11107  rexico  11786  cnntr  14955  2sqlem6  15855  eupth2lemsfi  16335  setindft  16586