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  1783  ssuni  3920  nnmordi  6727  omnimkv  7398  caucvgsrlemoffcau  8061  caucvgsrlemoffres  8063  facdiv  11046  facwordi  11048  bezoutlemmain  12632  bezoutlemaz  12637  bezoutlembz  12638  algcvgblem  12684  prmfac1  12787  infpnlem1  12995  mplsubgfileminv  14784  cncfco  15385  limccnpcntop  15469  limccoap  15472  bj-rspgt  16487