Theorem imim2d 54

Description: Deduction adding nested antecedents. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
imim2d.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
imim2d	⊢ (𝜑 → ((𝜃 → 𝜓) → (𝜃 → 𝜒)))

Proof of Theorem imim2d

Step	Hyp	Ref	Expression
1		imim2d.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	a1d 22	. 2 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜒)))
3	2	a2d 26	1 ⊢ (𝜑 → ((𝜃 → 𝜓) → (𝜃 → 𝜒)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  imim2  55  embantd  56  imim12d  74  anc2r  328  pm5.31  348  con4biddc  862  jaddc  869  hbimd  1619  19.21ht  1627  nfimd  1631  19.23t  1723  spimth  1781  ssuni  3910  nnmordi  6675  omnimkv  7339  caucvgsrlemoffcau  8001  caucvgsrlemoffres  8003  facdiv  10977  facwordi  10979  bezoutlemmain  12540  bezoutlemaz  12545  bezoutlembz  12546  algcvgblem  12592  prmfac1  12695  infpnlem1  12903  mplsubgfileminv  14685  cncfco  15286  limccnpcntop  15370  limccoap  15373  bj-rspgt  16259