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  4405  nneneq  7026  prarloclem3  7692  fzind  9570  exbtwnzlemshrink  10476  rebtwn2zlemshrink  10481  seq3fveq2  10705  seqfveq2g  10707  seq3shft2  10711  seqshft2g  10712  monoord  10715  seq3split  10718  seqsplitg  10719  seq3id2  10756  seqhomog  10760  seq3coll  11072  rexico  11740  cnntr  14907  2sqlem6  15807  setindft  16352