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  3938  nnmordi  6751  omnimkv  7449  caucvgsrlemoffcau  8118  caucvgsrlemoffres  8120  facdiv  11108  facwordi  11110  bezoutlemmain  12702  bezoutlemaz  12707  bezoutlembz  12708  algcvgblem  12754  prmfac1  12857  infpnlem1  13065  mplsubgfileminv  14904  cncfco  15505  limccnpcntop  15589  limccoap  15592  bj-rspgt  16607