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  858  jaddc  865  hbimd  1595  19.21ht  1603  nfimd  1607  19.23t  1699  spimth  1757  ssuni  3871  nnmordi  6601  omnimkv  7257  caucvgsrlemoffcau  7910  caucvgsrlemoffres  7912  facdiv  10881  facwordi  10883  bezoutlemmain  12290  bezoutlemaz  12295  bezoutlembz  12296  algcvgblem  12342  prmfac1  12445  infpnlem1  12653  mplsubgfileminv  14433  cncfco  15034  limccnpcntop  15118  limccoap  15121  bj-rspgt  15684