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  862  jaddc  869  hbimd  1619  19.21ht  1627  nfimd  1631  19.23t  1723  spimth  1781  ssuni  3910  nnmordi  6670  omnimkv  7334  caucvgsrlemoffcau  7996  caucvgsrlemoffres  7998  facdiv  10972  facwordi  10974  bezoutlemmain  12534  bezoutlemaz  12539  bezoutlembz  12540  algcvgblem  12586  prmfac1  12689  infpnlem1  12897  mplsubgfileminv  14679  cncfco  15280  limccnpcntop  15364  limccoap  15367  bj-rspgt  16205