Theorem pm2.43i 49

Description: Inference absorbing redundant antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.)

Hypothesis

Ref	Expression
pm2.43i.1	|- ( ph -> ( ph -> ps ) )

Assertion

Ref	Expression
pm2.43i	|- ( ph -> ps )

Proof of Theorem pm2.43i

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ph -> ph )
2		pm2.43i.1	. 2 |- ( ph -> ( ph -> ps ) )
3	1, 2	mpd 13	1 |- ( ph -> ps )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  sylc  62  impbid  129  ibi  176  anidms  397  pm2.13dc  890  hbequid  1559  equidqe  1578  equid  1747  ax10  1763  hbae  1764  vtoclgaf  2867  vtocl2gaf  2869  vtocl3gaf  2871  ifmdc  3646  elinti  3935  copsexg  4334  nlimsucg  4662  tfisi  4683  vtoclr  4772  ssrelrn  4920  issref  5117  relresfld  5264  f1o2ndf1  6388  tfrlem9  6480  nndi  6649  mulcanpig  7545  lediv2a  9065  seq3id3  10776  resqrexlemdecn  11563  ndvdssub  12481  bitsinv1  12513  nn0seqcvgd  12603  modprm0  12817  mplbasss  14700  fiinopn  14718  xmetunirn  15072  mopnval  15156  plyssc  15453  2lgsoddprm  15832  uspgrushgr  16019  uspgrupgr  16020  usgruspgr  16022  usgredg2vlem2  16062  ax1hfs  16614