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  865  jaddc  872  hbimd  1622  19.21ht  1630  nfimd  1634  19.23t  1725  spimth  1784  ssuni  3941  nnmordi  6762  omnimkv  7460  caucvgsrlemoffcau  8129  caucvgsrlemoffres  8131  facdiv  11125  facwordi  11127  bezoutlemmain  12719  bezoutlemaz  12724  bezoutlembz  12725  algcvgblem  12771  prmfac1  12874  infpnlem1  13082  mplsubgfileminv  14981  cncfco  15582  limccnpcntop  15666  limccoap  15669  bj-rspgt  16684