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  6670  omnimkv  7331  caucvgsrlemoffcau  7993  caucvgsrlemoffres  7995  facdiv  10968  facwordi  10970  bezoutlemmain  12527  bezoutlemaz  12532  bezoutlembz  12533  algcvgblem  12579  prmfac1  12682  infpnlem1  12890  mplsubgfileminv  14672  cncfco  15273  limccnpcntop  15357  limccoap  15360  bj-rspgt  16174