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  3909  nnmordi  6660  omnimkv  7319  caucvgsrlemoffcau  7981  caucvgsrlemoffres  7983  facdiv  10955  facwordi  10957  bezoutlemmain  12514  bezoutlemaz  12519  bezoutlembz  12520  algcvgblem  12566  prmfac1  12669  infpnlem1  12877  mplsubgfileminv  14658  cncfco  15259  limccnpcntop  15343  limccoap  15346  bj-rspgt  16108