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 ) ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used 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  3957  nnmordi  6793  omnimkv  7502  caucvgsrlemoffcau  8171  caucvgsrlemoffres  8173  facdiv  11198  facwordi  11200  bezoutlemmain  12800  bezoutlemaz  12805  bezoutlembz  12806  algcvgblem  12852  prmfac1  12956  infpnlem1  13167  mplsubgfileminv  15216  cncfco  15817  limccnpcntop  15901  limccoap  15904  bj-rspgt  17019