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  865  jaddc  872  hbimd  1622  19.21ht  1630  nfimd  1634  19.23t  1725  spimth  1784  ssuni  3935  nnmordi  6748  omnimkv  7446  caucvgsrlemoffcau  8109  caucvgsrlemoffres  8111  facdiv  11096  facwordi  11098  bezoutlemmain  12687  bezoutlemaz  12692  bezoutlembz  12693  algcvgblem  12739  prmfac1  12842  infpnlem1  13050  mplsubgfileminv  14842  cncfco  15443  limccnpcntop  15527  limccoap  15530  bj-rspgt  16545