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 )

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:  sylc  62  impbid  129  ibi  176  anidms  401  pm2.13dc  897  hbequid  1566  equidqe  1585  equid  1753  ax10  1769  hbae  1770  vtoclgaf  2888  vtocl2gaf  2890  vtocl3gaf  2892  ifmdc  3683  elinti  3979  copsexg  4384  nlimsucg  4713  tfisi  4734  vtoclr  4823  ssrelrn  4972  issref  5170  relresfld  5317  f1o2ndf1  6464  tfrlem9  6590  nndi  6759  mulcanpig  7703  lediv2a  9228  seq3id3  10976  resqrexlemdecn  11794  ndvdssub  12716  bitsinv1  12748  nn0seqcvgd  12838  modprm0  13056  mplbasss  15178  fiinopn  15196  xmetunirn  15550  mopnval  15634  plyssc  15931  2lgsoddprm  16398  uspgrushgr  16587  uspgrupgr  16588  usgruspgr  16590  usgredg2vlem2  16630  ax1hfs  17291