Theorem imim2d 54

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

Hypothesis

Ref	Expression
imim2d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
imim2d	|- ( ph -> ( ( th -> ps ) -> ( th -> ch ) ) )

Proof of Theorem imim2d

Step	Hyp	Ref	Expression
1		imim2d.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	a1d 22	. 2 |- ( ph -> ( th -> ( ps -> ch ) ) )
3	2	a2d 26	1 |- ( ph -> ( ( th -> ps ) -> ( th -> ch ) ) )

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  864  jaddc  871  hbimd  1621  19.21ht  1629  nfimd  1633  19.23t  1725  spimth  1783  ssuni  3915  nnmordi  6683  omnimkv  7354  caucvgsrlemoffcau  8017  caucvgsrlemoffres  8019  facdiv  10999  facwordi  11001  bezoutlemmain  12568  bezoutlemaz  12573  bezoutlembz  12574  algcvgblem  12620  prmfac1  12723  infpnlem1  12931  mplsubgfileminv  14713  cncfco  15314  limccnpcntop  15398  limccoap  15401  bj-rspgt  16382