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  865  jaddc  872  hbimd  1622  19.21ht  1630  nfimd  1634  19.23t  1725  spimth  1784  ssuni  3936  nnmordi  6749  omnimkv  7447  caucvgsrlemoffcau  8113  caucvgsrlemoffres  8115  facdiv  11100  facwordi  11102  bezoutlemmain  12694  bezoutlemaz  12699  bezoutlembz  12700  algcvgblem  12746  prmfac1  12849  infpnlem1  13057  mplsubgfileminv  14855  cncfco  15456  limccnpcntop  15540  limccoap  15543  bj-rspgt  16558