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  3231  ssralv  3288  soss  4406  nneneq  7031  prarloclem3  7700  fzind  9578  exbtwnzlemshrink  10485  rebtwn2zlemshrink  10490  seq3fveq2  10714  seqfveq2g  10716  seq3shft2  10720  seqshft2g  10721  monoord  10724  seq3split  10727  seqsplitg  10728  seq3id2  10765  seqhomog  10769  seq3coll  11082  rexico  11753  cnntr  14920  2sqlem6  15820  setindft  16437