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  326  pm5.31  345  con4biddc  842  jaddc  849  hbimd  1552  19.21ht  1560  nfimd  1564  19.23t  1655  spimth  1713  ssuni  3753  nnmordi  6405  omnimkv  7023  caucvgsrlemoffcau  7599  caucvgsrlemoffres  7601  facdiv  10477  facwordi  10479  bezoutlemmain  11675  bezoutlemaz  11680  bezoutlembz  11681  algcvgblem  11719  prmfac1  11819  cncfco  12736  limccnpcntop  12802  limccoap  12805  bj-rspgt  12982