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  6789  omnimkv  7496  caucvgsrlemoffcau  8165  caucvgsrlemoffres  8167  facdiv  11176  facwordi  11178  bezoutlemmain  12775  bezoutlemaz  12780  bezoutlembz  12781  algcvgblem  12827  prmfac1  12930  infpnlem1  13138  mplsubgfileminv  15091  cncfco  15692  limccnpcntop  15776  limccoap  15779  bj-rspgt  16814