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  892  hbequid  1561  equidqe  1580  equid  1749  ax10  1765  hbae  1766  vtoclgaf  2869  vtocl2gaf  2871  vtocl3gaf  2873  ifmdc  3648  elinti  3937  copsexg  4336  nlimsucg  4664  tfisi  4685  vtoclr  4774  ssrelrn  4922  issref  5119  relresfld  5266  f1o2ndf1  6392  tfrlem9  6484  nndi  6653  mulcanpig  7554  lediv2a  9074  seq3id3  10785  resqrexlemdecn  11572  ndvdssub  12490  bitsinv1  12522  nn0seqcvgd  12612  modprm0  12826  mplbasss  14709  fiinopn  14727  xmetunirn  15081  mopnval  15165  plyssc  15462  2lgsoddprm  15841  uspgrushgr  16030  uspgrupgr  16031  usgruspgr  16033  usgredg2vlem2  16073  ax1hfs  16685