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  7497  caucvgsrlemoffcau  8166  caucvgsrlemoffres  8168  facdiv  11192  facwordi  11194  bezoutlemmain  12794  bezoutlemaz  12799  bezoutlembz  12800  algcvgblem  12846  prmfac1  12950  infpnlem1  13161  mplsubgfileminv  15182  cncfco  15783  limccnpcntop  15867  limccoap  15870  bj-rspgt  16980