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  869  jaddc  876  hbimd  1626  19.21ht  1634  nfimd  1638  19.23t  1729  spimth  1788  ssuni  3952  nnmordi  6779  omnimkv  7486  caucvgsrlemoffcau  8155  caucvgsrlemoffres  8157  facdiv  11154  facwordi  11156  bezoutlemmain  12753  bezoutlemaz  12758  bezoutlembz  12759  algcvgblem  12805  prmfac1  12908  infpnlem1  13116  mplsubgfileminv  15014  cncfco  15615  limccnpcntop  15699  limccoap  15702  bj-rspgt  16728